 x 1 vector S = S1 and the MIMO encoder generates the 1 X 2 CDR vector X = [s1 s*]. = The CDR matrix occupies two consecutive sub-carriers in the frequency domain. For horizontal encoding and vertical encoding, the input and the output of the MIMO encoder is represented by an M X 1 vector X = S = [S1,S2,...,SM]' where modulated symbol in the input block. In the case of vertical encoding S1,S2,...,SM belong to the same layer and the MIMO encoder is an identity operation, whereas for horizontal encoding S1,S2, belong to different layers. Note that multi-layer encoding is only used in conjunction with MU-MIMO schemes. The number of streams depends on the MIMO encoder. For open-loop and closed-loop 10.5 IEEE 802. 16m downlink MIMO schemes spatial multiplexing SU-MIMO, the number of streams is N5 min(N, Nr), N < 8. For open-loop transmit diversity, N depends on the space-time coding scheme that is used by the MIMO encoder. The IEEE 802.16 MU-MIMO supports up to two spatial streams with two transmit-antennas and up to four spatial streams for four and eight transmit antennas. Stream to antenna mapping is performed by the precoder block. The output of the MIMO encoder multiplied by N X NS precoding matrix W. The output of the precoder block is denoted by the N X Nf matrix Z as follows: Z=Wx = = (10-50) Where Nf denotes the number of sub-carriers occupied by one MIMO block and Zjk is the output complex-valued symbol to be transmitted by the jth physical antenna on the kth sub-carrier. The pilot sub-carriers within a physical resource unit are precoded in the same way as the data sub-carriers. The successive symbols at the output of the precoder block are mapped to the corresponding antenna ports. The sub-carrier mapping within a logical resource unit starts from the data sub-carrier with the lowest OFDM symbol index and lowest sub-carrier index, and continues with increasing sub-carrier index. If the edge of the resource unit is reached, the mapping is continued on the next OFDM symbol. Non-adaptive precoding is used wit