to use the channel samples estimated at the pilot tones to reconstruct channel samples at the remaining data tones. As a result, the pilot pattern design is essentially a conventional sampling rate selection problem in two-dimensional signal processing. In order to avoid aliasing during reconstruction of the channel time-frequency func- tion, the pilot tone selection should follow the two-dimensional sampling theorem. When multiple antennas are used, the receiver must estimate the channel impulse response (or the transfer function) from each of the transmit antennas in order to correctly detect the signal. This is achieved through distributing reference signals (or pilot tones) or MIMO midamble among the transmit antennas. Let 1/T and Ts denote the sub-carrier spacing and the OFDM symbol duration (inclusive of the guard interval), respectively. Let's further assume that the pilot sub-carriers are transmitted at integer multiples of sub-carrier spacing and OFDM symbol duration in frequency and time directions, respectively (i.e., fp = m/T and Tp = nTs where m and n are integers). The (m, n) pair represent the pilots' separation in terms of sub-carrier spacing and OFDM symbol duration. From CHAPTER 9 The IEEE 802. 16m Physical Layer (Part I) the sampling theorem point of view, the channel's two-dimensional delay-Doppler response h(t, v) can be fully reconstructed, if the two-dimensional transform function H(t,f) is sampled at greater than or equal to the Nyquist rate across time and frequency dimensions. Hence, the time-domain sampling rate must be greater than or equal to the channel's maximum Doppler spread, i.e., Tp < 1/V max (the sampling rate in time must be less than the coherence time) and the frequency-domain sampling rate must be greater than or equal to the channel's maximum delay spread, i.e., fp < 1/T max (the sampling rate in frequency must be less than the coherence bandwidth). Assuming a wide-sense stationary uncorrelated scattering channel model and assuming the channel to be constant over one OFDM 