# In a coded and interleaved FH q-ary FSK modulation with partial band jamming and coherent…

In a coded and interleaved FH q-ary FSK modulation with partial band jamming and coherent demodulation with soft-decision decoding, the cutoff rate is

where α is the fraction of the band being jammed, Ec is the chip (or tone) energy, and N0 = J0.

a. Show that the SNR per bit can be expressed as

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

c. Define r = R0/R in the result for εb/N0 from (b), and plot 10 log(εb/r N0) versus the normalized cut off rate R0/ log2 q for q = 2, 4, 8, 16, 32. Compare these graphs with the results of Problem 12.30c. What conclusions do you reach regarding the effect of worst-case partial band jamming? What is the effect of increasing the alphabet size q? What is the penalty in SNR between the results in Problem 12.30c and q-ary FSK as q → ∞?

Problem 12.30c

c. Plot the graph of 10 log(εb/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?