In the mid$-1970$s$,$ the US Army was developing a tactical radio system known

as SINCGARS, to be carried by a soldier in the field. One of the desirable

features of the system was the ability to hop from frequency to frequency to

avoid jamming. This is an ECCM $($Electronic Counter$-$countermeasues$)$

technique known as FHSS $($Frequency Hopping Spread Spectrum$).$ Obviously,

the faster the radio could hop between channels the harder the work would be

for the enemy to follow the radio and jam in on its operating channel. If FHSS were successful, the best the enemy could do would be to jam the entire range

of frequencies, putting a small fraction of their total power on any one

frequency. The radio was capable of operating from $3088$ MHz$,$ and could

tune in $25$ kHz steps. The use of FHSS impacts several radio subsystems $$

the synthesizer, the PA$,$ the antenna tuning, the antenna, to name a few.

Discuss the practical implications of frequency hopping on the radio design and

estimate the fastest rate that a radio might be able to hop from channel to

channel. Suggest ways to increase that speed. Assume that the radio will be

called on to hop from f$1$ to f$2$ where both f$1$ and f$2$ can be arbitrarily taken from

the set of frequencies $\{30\mathrm{.}000,30\mathrm{.}025,30\mathrm{.}050,...,87\mathrm{.}950,87\mathrm{.}975,88\mathrm{.}000),$ that

is the radio at times might hop from the lowest to the highest channel in the set,

or vice versa.