sed can be dynami- cally changed on a subframe basis according to the channel feedback reports from the UE. The precoder matrix describes the mapping of the different layers to the antenna ports (the relation between Y and x)-that is, =WWxx. C 2009 by Taylor & Francis Group, LLC Long Term Evolution: 3GPP LTE Radio and Cellular Technology The codebook-based precoding is one of the primary transmission modes in LTE. The standard defines one codebook for the two-transmit-antenna case and one for the four-transmit-antenna case. For more details on the actual codebooks, see 3GPP TS 36.211 [5]. The precoding can be further combined with CDD transmission, where the mapping of the symbols from the layers to the antenna ports is done by the pre- coder matrix and the CDD matrix together (i.e., Y = D(k) W(i) X, where D(k) is the transform matrix performing the CDD operation: e-j2tk8 D(k) = e-j2rk28 -j2nk38 where k represents the frequency domain index of the resource element to which the transmission is mapped and 8 is the delay shift. The idea with the CDD trans- formation is to employ an increasing phase shift on the antenna ports. Depending on the actual channel matrix, on some antenna ports the phase shift will match the actual channel and thereby result in an increased SINR; on other antenna ports, it may null out the transmission, constituting a source of diversity. In beam forming, a single symbol is multiplied by different weight factors and sent on the different antenna elements; this introduces antenna-specific phase adjust- ments. As a result of the different phase adjustments on the different antennas, the transmitted signal can be steered in specific directions. That is, the "precoding" operation for beam forming, assuming four transmit antennas, is the following: where X is the modulation symbol corresponding to the single layer. The preceding transmit diversity, spatial multiplexing, and beam-forming schemes apply for the downlink directions only. In the uplink, there is only a lim- ited set of multiantenna t