ly transmitted data streams from the received signals, denoted as Yj. Additionally, if some knowledge of the MIMO channel is available at the transmitter, the different parallel channels can be made independent of each other, © 2009 by Taylor & Francis Group, LLC Long Term Evolution: 3GPP LTE Radio and Cellular Technology Stream 1 Stream 1 Stream 2 Stream 2 Processing Processing Stream K Stream K MIMO Channel Matrix (H) Figure 3.21 Spatial multiplexing of different data streams over different trans- mit antennas. thus reducing significantly the interfering signals at the receiver. This is possible by means of closed-loop- or precoding-based spatial multiplexing, as discussed in Section 2.3. The theoretical maximum rate increase factor is L in a rich scattering environment with high spatial diversity (i.e., uncorrelated paths). However, there is no appreciable gain with a predominant line-of-sight component or, equivalently, when a high cor- relation between different paths occurs. Under such conditions, the received signals have no spatial signature and the originally multiplexed signals cannot be recovered at the receiver (parallel transmission of data streams becomes unfeasible). Therefore, spatial multiplexing is strongly conditioned by the MIMO channel matrix (H). From an algebraic point of view, the rank of H determines the maxi- mum achievable number of spatially multiplexed signals-that is, the number of parallel channels for reliable data transmission. Assuming R to be the rank of H, the number of multiplexed data streams or spatial multiplexing order (K) must satisfy: K<R<L (3.1) That is, the multiplexing gain is limited to the rank of the channel matrix. It is clear from Equation (3.1) that when H has full rank (i.e., R = L-for example, in a rich scattering scenario), the maximum theoretical gain can be achieved. However, highly correlated paths imply that H is ill conditioned or rank deficient, SO the spa- tial multiplexing order (number of multiplexed data streams) may be significantly limited. In gen