na port #N Mapper Mapper Generation Figure 4.16 MIMO transmit processing chain. © 2009 by Taylor & Francis Group, LLC Architecture and Protocol Support for RRM with the column vector x(i). For example, the layer mapping in the case of spatial multiplexing, assuming four transmit antennas and two code words, looks like the following: x(i) = The precoder takes the output vectors of the layer mapper one by one (denoted by X from now on; for simplicity we omit the index i) and generates a matrix of Y with size of NxR, where N is the number of transmit antennas and R is the num- ber of resource elements on which the L layers are transmitted. That is, the precoder encodes the layers into a block of vectors, where the first dimension of the encoded block is the transmit antennas (spatial domain) and the second dimension can be the time or the frequency domain, resulting in STBC or SFBC, respectively. In other words, the columns of the matrix Y correspond to what is transmitted on the respective transmit antennas on one given time-frequency resource element. The resource elements to which the different columns of the matrix are mapped can be in the same subframe but on different carrier frequencies (SFBC case), or they can be in different subframes (STBC case). In LTE, only the SFBC type of precoding is applied. In the simplest case, the matrix Y can be a single vector, meaning that the layers are only spatially encoded but not in the time or the frequency domain. Next, we show examples for the precoding operation for the different spatial multiplexing and diversity schemes used in LTE. The precoder operation for transmit diversity is defined for two and four antenna ports and has the following form (two-antenna-ports case): where the notation C denotes the complex conjugate. This type of precoding is also called Alamouti coding and corresponds to SFBC. Precoding for spatial multiplexing typically involves a set of precoder matrices, {W(1), W(2),..., W(K)}, also called a codebook, where the actual precoder matrix to be u