A channel of bandwidth 4 MHz is available through which it is desired to communicate at a data rate of 1 Mbps.

(a) Find the largest value of M, which is a power of 2, for M-ary coherent FSK such that this is possible.

(b) Find the value of E_b / N₀ in dB necessary to provide P_b = 10^-4 for the allowed value of M found in part (a).

(c) Repeat part a for M-ary non-coherent FSK.

(d) Find the value of E_b / N₀ in dB necessary to provide P_b = 10^-4 for the allowed value of M found in part (c).

(e) Comment on the price paid for the simplicity of not having to establish a coherent reference at the receiver in order to use non-coherent modulation.