Pulse jamming and soft-decision decoding

Question

Solve the following problem:

In coded and interleaved DS binary PSK modulation with pulse jamming and soft-decision decoding, the cutoff rate is

R₀ = 1 - log₂( 1 + ae^-αε_c/N₀)

where α is the fraction of the time the system is being jammed, E_c = ε_bR, R is the bit rate, and N₀ ≡ J₀.

a. Show that the SNR per bit, ε_b/N₀, can be expressed as

ε_b/N₀ = 1/αR  In  α/2^1-R₀ - 1

b. Determine the value of α that maximizes the required ε_b/N₀ (worst-case pulse jamming) and the resulting maximum value of ε_b/N₀.

c. Plot the graph of 10 log(ε_b/r N₀) versus R₀, where r = R₀/R, for worst-case pulse jamming and for AWGN (α = 1). What conclusions do you reach regarding the effect of worst-case pulse jamming?