Impact of Spatial Correlation on Orthogonal Precoding for MIMO transmissions in tunnels Kamel Boukantar 1, , Charlotte Langlais 2 , Yann Cocheril 1 and Marion Berbineau 1 1 Univ Lille Nord de France, F-59000 Lille, INRETS, LEOST, F-59650 Villeneuve d’Ascq firstname.name@inrets.fr 2 Institut TELECOM ; TELECOM Bretagne ; UMR CNRS 3192 Lab-STICC Electronic Engineering department, Technopole Brest Iroise, CS 83818, 29238 Brest Cedex 3, France Universit´ e Europ´ eenne de Bretagne firstname.name@telecom-bretagne.eu Abstract—Multiple-input Multiple-output (MIMO) techniques have proven their potentiality for transmissions in the tranport domain even in specific contexts, such as tunnels. When perfect channel state information (CSI) is available at the transmitter, performance improvement is allowed through a precoding oper- ation. However, the performance of such a closed-loop MIMO system depends on the spatial correlation in the channel, the quantity and the quality of the CSI. A perfect knowledge of the CSI is rarely available in practice because the CSI usually undergoes various impairments, such as channel estimation errors and quantization errors. To overcome these drawbacks, we propose the investigation of two limited feedback precoders that allow us to reduce simultaneously processing complexity and the amount of feedback information. The first, OSM is based on the orthogonalization of the channel and the second is the basic quantized single beamforming based on the Grassmannian line packing technique. The comparison is performed both for an ideal Rayleigh channel and for two typical transmission scenarios in tunnels. Simulation results show that the OSM precoder achieves better performances than the unprecoded scheme, whatever the level of correlation in tunnels. Quantized single beamforming is interesting only for the high-correlated scenario. In this case it outperforms the OSM scheme and the unprecoded scheme. I. I NTRODUCTION MIMO systems have received significant attention over the last ten years due to their capability of providing high data rates through spatial multiplexing [1] and diversity through space-time coding [2] or beamforming [3]. This technology is nowadays an essential part of many emerging 3G/4G wireless telecommunication standards and is considered a good solution for robust and high date rate communications in transport applications, even though the performances depend on the spatial correlation in the channel [4]. In this paper we consider MIMO communications for mass transit applications in tunnels where it is proven that the variation of the correlation degree depends on the transmitter-receiver distance and the movement of the vehicle [5]. However, it is shown in [6] that the temporal variations of the channel characteristics dictate the requirements for adaptive transmission. The channel state information at the transmitter (CSI-T) enhances MIMO system performances by increasing spectral efficiency and/or reducing error probability by using a precoder at the transmitter. Based on perfect CSI-T, precoders are proposed in [7], [8], [9] for many different design criteria. Most of the precoder designs are based on the singular value decomposition (SVD) of the channel matrix. In the SVD-based scheme, the right singular vectors of the channel matrix are fed back to the transmitter, but the consequence is extra bandwidth consumption at the feedback link. To address this issue, low-rate feedback schemes that achieve performances close to the one of precoding schemes with perfect CSI-T have been introduced in [10], [11]. A codebook of precoding matrices is created offline both at the transmitter and at the receiver. The receiver chooses the optimal precoder matrix from the codebook and the only feedback parameter is the index of the appropriate matrix. The computational complexity of the SVD operation becomes problematic with the increased number of transmit and receive antennas due to the iterative nature of the SVD computation. Therefore, a limited feedback precoder for orthogonalized spatial multiplexing (OSM) systems has been developed in [12]. It achieves orthogonality between transmitted symbols by applying a phase rotation at the transmitter. Compared to SVD-based precoders, the OSM scheme exhibits better system performance with lower complexity and feedback overhead. Recently, the authors have proposed an optimized scheme for the OSM precoder that can improve the performance substantially [13] and offer an additional diversity gain by using a two-step processing. However, the performance of such closed-loop MIMO systems depends on the spatial correlation in the channel, the quantity and the quality of the CSI. A perfect knowledge of the CSI is rarely available in practice because the CSI usually undergoes various impairments, such as channel estimation errors and feedback errors.