ant over (at least) two consecutive symbol periods. Appropriate processing at the receiver, as shown in Equations (10-33) and (10-34), collapses the vector channel into a scalar channel for either of the transmitted data symbols where r is the processed received signal corresponding to transmitted symbol S and ñ is the processed noise. Even though the channel knowledge is not available to the transmitter, the Alamouti scheme achieves 2Nr order diversity. We note, however, that array gain is realized only at the receiver since the transmitter does not have channel state information. The Alamouti scheme may be extended to channels with more than two transmit antennas through orthogonal space-time block coding. The link-level performance of the Alamouti scheme is compared to the SISO and SIMO cases in Figure 10-27, assuming BPSK-modulated input symbols and Rayleigh fading channel. CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) N+=1,N,=1 (SISO) Nt=1,N,=2 (SIMO with MRC) Nt=2,N,=1 (Theoretic Alamouti) N=2,N=1 (Simulated Alamouti) 10- -5 Eb/No (dB) FIGURE 10-27 Performance of the Alamouti scheme Delay diversity is an alternative method in which the same symbol is transmitted at different time instances, such that each symbol experiences different fading. The delay diversity converts spatial diversity into frequency diversity by transmitting the data signal from the first antenna port and a delayed replica of the signal from the second antenna port. Assuming two transmit antennas and one receive antenna and the delay induced by the second antenna equals one symbol period, the effective channel seen by the data signal is a frequency-selective fading SISO channel with impulse response h (k) = h1d(k) + h2d(k - 1) where h1 and h2 are complex-valued flat-fading channels. We note that the effective channel resembles a two-path SISO channel with independently fading paths and equal average path energy. A Maximum-Likelihood (ML) detector will realize full second-order diversity at the receiver. If the same signal is tran