generated due to frequency reuse in wireless channels. When multiple antennas are used, the differentiation between the spatial signatures of the desired signal and co-channel signals can be utilized to reduce interference. While interference cancellation requires proper knowledge of the desired signal's channel, exact knowledge of the interferers' channels may not be necessary. Interference avoidance schemes can also be implemented at the transmitter where the goal is to minimize the interference energy sent toward the co-channel users while delivering the signal to the desired user. Interference reduction allows aggressive CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) frequency reuse, and thereby increases multi-cell capacity. It must be noted that not all advantages of MIMO schemes can be simultaneously achieved due to conflicting demands on the spatial degrees of freedom or the number of transmit and/or receive antennas. The degree to which these conflicts can be resolved depends on the signaling scheme and transceiver design. 10.4.1 Capacity of MIMO Channels As shown in Figure 10-22, a generic MIMO system consists of a MIMO transmitter with N transmit antennas, a MIMO receiver with Nr receive antennas, and Nr X N paths or channels between the transmit and receive antennas. Let xk(t) denote the transmitted signal from the kth transmit antenna at time t, then the received signal at the 1th antenna can be expressed as follows: (10-21) where hik(t) and ni(t) are the channel impulse response between the kth transmit and 1th receive antenna and the additive noise at the 1th receive antenna port, respectively. The above equation can be written in the frequency-domain as Y1(w)Hk(w)Xk(w)+N1(w) (10-22) If x(w) n(w) = [N1 (w), denote the Fourier transform vectors of xk(t), yi(t), and ni(t), respec- tively, then y(w) = H(w)x(w) n(w) where H(w) is an N1 X N channel matrix with entries. TX Ant 1 Ant 1 TX Ant 2 RX Ant 2 Transmitter Receiver TX Ant Nt RX Ant Nr hNrNt (MIMO Channel) FIGURE 10-22 An illustration of th