An Orthogonal Frequency Division Multiplexing (OFDM) based wireless communication system is allocated 25 MHz channel, with number of carriers, = 128, of which 4 carriers on each side at the band edges are nulled, and 6 carriers are used as pilots. The system supports M-ary Quadrature Amplitude Modulation (M-QAM) modulation and code rates of 1/2, 2/3 and 3/4. a. If the system is required to handle a maximum delay spread of 1 s, calculate the appropriate number of samples required for the cyclic prefix. b. Calculate the frequency separation between sub-carriers AND determine the OFDM symbol time. c. If the system is required to achieve a data rate of at least 30 Mbits/s, find the most appropriate modulation order and code rate. d. What is the function of the pilot and nulled sub-carriers described above?