1 Analysis of the Spatial Correlation of Indoor MIMO PLC Channels Julio A. Corchado, Jos´ e A. Cort´ es, Francisco J. Ca˜ nete, Antonio Arregui and Luis D´ ıez Abstract—In this paper, an analysis of the spatial correlation of multiple-input multiple-output (MIMO) power line commu- nications (PLC) channels in the frequency range 1-80 MHz is provided, where the term spatial correlation refers to the relation between the paths that form the MIMO channel matrix. The study is based on a large set of 2x2 MIMO channels measured in four different countries. The presented statistical analysis of the condition number reveals three important facts. First, that the spatial correlation is almost independent of frequency, which has important implications in the development of top-down MIMO PLC channel models. Second, that the use of an alternative injection method can notably reduce the spatial correlation and, consequently, increase the system bit-rate. Third, that there exist countries whose channels have larger spatial correlation values than others. Since spatial correlation plays a key role in the performance of MIMO PLC systems, a hypothesis relating the type of wiring deployed in the indoor power grid to the spatial correlation is given and supported by simulations. Index Terms—MIMO, wiring, PLC, spatial correlation I. I NTRODUCTION In recent years, PLC has become a valuable solution to provide many services, like the support of local area networks (LAN)s and the transmission of high-speed multimedia con- tent, in a cost-effective manner as it takes advantage of the already deployed power grid. In many countries, the majority of modern indoor power networks have three conductors: phase (P), neutral (N) and protective earth (E). This allows exploiting the MIMO capability of the channel by using differential transmission among conductors. Accordingly, the latest releases of PLC systems specifications include MIMO techniques [1], [2]. Studies carried out in the last years have analyzed charac- teristics of MIMO PLC channels such as the attenuation, delay spread and spatial correlation [3]–[6]. Channel models derived from measurements, referred to as top-down, and obtained from a model of the physical structure of the power grid, known as bottom-up, have been proposed [3], [5], [7]–[9]. In this context, the present work makes four contributions: • It verifies that the spatial correlation is frequency inde- pendent, which notably simplifies the development of top- down MIMO PLC channel models. • It shows that the spatial correlation can be reduced by modifying the injection mode. This result suggests a J. A. Corchado, J. A. Cort´ es, F. J. Ca˜ nete and L. D´ ıez are with the Departamento de Ingenier´ ıa de Comuniaciones, Escuela T´ ecnica Superior de Ingenier´ ıa de Telecomunicaci´ on, Universidad de M´ alaga, 29010 M´ alaga, Spain (e-mail: julioalc, jaca, francis, diez@ic.uma.es). A. Arregui is with Marvell Hispania S.L., Paterna, 46980 Valencia, Spain (e-mail: aarregui@marvell.com). simple way of enhancing the performance of MIMO PLC systems without increasing their complexity. • It reveals that there are countries whose channels have lower spatial correlation values than others, which implies that MIMO PLC systems might perform better in some countries than in others. • It demonstrates that differences in the spatial correlation between countries can be largely due to the type of cabling deployed in their respective indoor power grids. This fact provides an a priori (without measurements) criterion to compare the performance that a given MIMO PLC system would attain in different indoor networks. It also highlights that top-down channel models should be parametrized differently depending on the type of cabling employed in the power grids under study. Presented results are based on a measurement campaign car- ried out in four European countries. Channels were registered in the frequency band 1-100 MHz, but the analysis is restricted to the range 1-80 MHz to avoid the FM broadcast band. The remainder of the paper is organized as follows. Section II presents the spatial correlation concept along with an analysis, carried out over measured channels, of its dependence on frequency and on the injection mode. Section III firstly shows that there are countries whose MIMO channels exhibit lower correlation values than others. Then, a hypothesis for this behavior is given and supported by means of simulations. Finally, in Section IV, conclusions are drawn. II. CHANNEL SPATIAL CORRELATION ANALYSIS A. Definition of Spatial Correlation In this section, the spatial correlation of MIMO PLC chan- nels is studied. The spatial correlation term has been adopted from the multiple-antenna wireless argot. The idea behind multiple-antenna configurations is that channels between each pair of transmitting and receiving antennas can be considered statistically independent. Thus, theoretically, multiple indepen- dent channels can be created, by means of some techniques such as precoding, which can then be exploited to improve link reliability and throughput [10]. In practice, full potential multi- antenna gains are not achievable because channels between each pair of transmitting and receiving antennas are not truly independent, but they are correlated to a certain degree. The closer antennas are deployed, the stronger the (spatial) correlation between channels is. Spatial correlation can be seen as an indicator of the achievable gain in MIMO channels: the lower the spatial correlation, the higher the potential gain is [10]. In PLC, the