100 3G Evolution: HSPA and LTE for Mobile Broadband of the signal-to-noise ratio. In such a case, the multiple transmit and receive antennas should be used for beam-forming to improve the signal-to-noise ratio, rather than for spatial multiplexing. In more general case, the spatial-multiplexing order should be determined based N on the properties of the size N R T channel matrix. Any excess antennas should then be used to provide beam-forming. Such combined beam-forming and spatial multiplexing can be achieved by means of pre-coder-based spatial multiplexing, as discussed below. 6.5.2 Pre-coder-based spatial multiplexing Linear pre-coding in case of spatial multiplexing implies that linear processing by means of a size N T N L pre-coding matrix is applied at the transmitter side as illustrated in Figure 6.16 . In line with the discussion above, in the general case N L is equal or smaller than N T , implying that N L signal are spatially multi- plexed and transmitted using N T transmit antennas. It should be noted that pre-coder-based spatial multiplexing can be seen as a