oding matrix Wk is selected from a subset of size Nw precoders derived from the base codebook for a given rank and changes every uPsc sub-carriers and every V subframes in order to provide additional spatial diversity. The values of and V depend on the MIMO scheme and type of resource unit [2]. The values of Nw for non-adaptive pre- coding and different subchannelization schemes are given in Table 10-28. No precoding function is utilized at an MS with one transmit antenna. For adaptive precoding, the precoding matrix W is derived at the BS or at the MS per instructions by the BS. Unitary codebook-based adaptive precoding is supported with two or four transmit antennas at the MS in FDD and TDD modes. In this mode, the MS transmits a sounding signal on the uplink to assist the precoder selection at the BS. Based on the measurements of the sounding channel at the BS, the BS indicates the uplink precoding matrix index to be used by the MS in a downlink control message. Adaptive precoding based on the measurement of downlink reference signals can be per- formed with two or four transmit antennas at the MS in TDD systems. The MS chooses the precoder based on the downlink measurements. The form and derivation of the precoding matrix does not need to be known at the BS. In the uplink SU-MIMO and MU-MIMO modes, all demodulation pilots precoded in the same way as the data, regardless of the number of transmit antennas, allocation type, or MIMO mode. There are five uplink MIMO modes for traffic and control channels that are listed in Table 10-29. The uplink MIMO parameters are given in Table 10-30 and Table 10-32. Table 10-28 Size of the Uplink Subset Codebooks (Nw) Uplink Subchannelization Type Type of Precoding Uplink distributed LRU and Non-adaptive Nt = 2 mini-band LRU Uplink sub-band LRU Nt = 4 10.6 The IEEE 802. 16m uplink MIMO schemes Table 10-29 Uplink MIMO Modes [2] Mode Index Description MIMO Encoding Format MIMO Precoding Mode 0 Open-loop SU-MIMO Non-adaptive Mode 1 Open-loop SU-MIMO (spatial Vertical encoding No