Question

In coherent schemes, a small pilot is added for synchronization. Because the pilot does not carry information, it causes degradation in P. Consider a coherent PSK that uses the following two pulses of duration Tg: p(t) = AV1 - m2 cos wet +A m sin wet 4(t) = -AVI - m² cos wet + Am sin wet Ep + Eq – 2Epg Problems 60 where Am sin wut is the pilot. Show that when the channel noise is white Gaussian, |2Eg{1 – m²) P = Q

Answer 1

Solution:

Given that:

P(t)=A$\sqrt{}$1-m ²  COS ${\omega }$ ct +A m Sin ${\omega }$ ct  

and q(t)=-A$\sqrt{}$1-m ²COS ${\omega }$ ct +A m Sin ${\omega }$ ct ,

where A m Sin ${\omega }$ ct is the pilot.
Solution : Given that Plt) = Ati-mo? Cos wet + Am Sin wat VEL) -- AVI-m? Cos wet + Am Sin Wet pimos años * (pre) – Pes Jºdt - Ep+ Eq, - 2 Epp The Energy of plt) is 'To times the power of Hence, Ep= 1 Pets a ? 1 ) tot ni pare to the En Steilarly, Egr En CiumiTor Apt - En Fru s per gent - LE (19") continue to A’m? sin" wet]dt --A Tin + a?n? To Hence, pr man = ²To b + A² Tb + 2 A Tb - 24 m To 2 2 2 NL2

Boman = 4A TO (1-m) 866(1-m2) M and fo = a (tot) AM