ed. The MIMO schemes can be used with non-OFDM systems when the channel is modeled as flat-fading such that: (10-25) An important question is to what extent MIMO techniques can increase the throughput and improve the reliability of wireless communication systems. This question can be answered by calculating the information theoretic capacity of a Single-Input Single-Output (SISO) channel and comparing with that of Single-Input Multiple-Output (SIMO), Multiple-Input Single-Output (MISO), and MIMO channels. For a memoryless SISO channel (i.e., one transmit and one receive antenna), the channel capacity is given by (10-26) where h is the normalized complex-valued gain/attenuation of a fixed wireless channel or that of a particular realization of a random channel and r denotes the SNR at any receive antenna port. As the number of receive antennas increases, the statistics of channel capacity improve. Using Nr receive antennas and one transmit antenna, a SIMO system is formed with a capacity given by: (10-27) CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) where hi is the gain of the ith channel corresponding to the ith receive-antenna. Note that increasing the value of N results in a logarithmic increase in average channel capacity. In the case of MISO or transmit diversity, where the transmitter usually does not have knowledge of the channel, the capacity is given by: (10-28) The power normalization factor N ensures that the total transmit power is uniformly distributed among the transmit antennas, and the absence of an array gain in this case (MISO) compared to a receive diversity scenario where the energy of the multipath channels can be coherently combined. In addition, the MISO capacity has a logarithmic relationship with N similar to that of a SIMO scheme. The use of diversity at both transmitter and receiver ends gives rise to a MIMO system. The capacity of a MIMO system with N transmit antennas and N receive antennas is expressed as follows: CMIMO (10-29) where I is an Nr X N1 identity matrix and H is t