symbol, the frequency response H(t, f) of the L-path channel is given as [46-48]: (9-18) Where 41, V1, and T1 denote the phase, Doppler frequency, and delay of the 1th path, respectively. All of these parameters are independent random variables. In general, the pilot signals are over-sampled in order to ensure a good trade-off between performance and overhead. Therefore, the choice of (m, n) depends on the channel's maximum delay spread and maximum Doppler spread and must satisfy the following equation according to the two-dimensional sampling theorem [25]: (9-19) It should be noted that the pilot density for a regular pattern can be calculated using Equation (9-19). From Equation (9-19), it can be seen that for large values of Vmax (i.e., large Doppler spread or alternatively small channel coherence time means that channel is time-varying), n should be small in order to appropriately track channel time variations. On the other hand, for large values of T max (i.e., large delay spread or alternatively small coherence bandwidth means that channel is frequency- selective), m should be small in order to follow channel frequency variation closely. In a regularly- spaced pilot pattern, the pilot symbols are evenly spaced in frequency and in time. Using the default OFDM symbol duration and the sub-carrier spacing given in Table 9-2 (OFDMA parameters Ts = 102.86 us and 1/T = 10.94 kHz), and assuming that the channel maximum delay spread Tmax = 5 us for the radio channels under consideration in the IEEE 802.16m evaluation methodology document, the most appropriate range for the values of (m,n) can be determined. Since the IEEE 802. 16m system is required to support vehicle speeds up to 350 km/h, the maximum Doppler spread is estimated as Vmax = 810 Hz at 2.5 GHz RF carrier frequency. From Equation (9-19) and the above design parameters, the following pilot spacing constraints are obtained n < 6, m < 9. Figure 9-32 illustrates a regularly-spaced two-dimensional pilot pattern for one spatial stream in the time frequency-do