View the step-by-step solution to:

1 Consider a binary digital communication system with received signal levels 1311 and mu for a 1 hit and [l hit1 respectively. Let drift and .53...

Hi could you please answer this question:

Untitled.png

This is the textbook solution to it: HOWEVER I do not know how the solution got those steps as its not very clear the steps. Ive highlighted in red. Could you please write the step by step solution of how the red parts were achieved. PLEASE ONLY ANSWER STEP BY STEP. Thank you



Untitleds.png

Untitled.png

1 Consider a binary digital communication system with received signal levels 1311
and mu for a 1 hit and [l hit1 respectively. Let drift and .53 denote the noise variances for a 1 and [I hit, respectively. Assume that the noise is Gaussian and that a 1 and [I
hit are equally likely. In this lease1 the bit error rate is given by —T 1 T -
“11 s) +—Q( d Win)l
0'1 Jr: 1 where T5 is the reoeiv'er‘s decision threshold. Show that the value of Ta that minimizes
the bit error rate is given by T mm: + ms+1/a§a§[<m1 — mar + 2 (a? — a3) Intense]
. = —. 2_ 2
51 an

Untitleds.png

BER=lQ ”PT“ +19 T‘f‘m” ,
2 m 2 an From this expression, for large lel, BER —3~ 1,32, so that an optimum Tar that minimizes the BER
exists. Setting BEERfflTd = I], we get, which can be written as {0'12 — fingj + 2(mm'5 — mwaTd +mfio'l2 — nailing” — 253512 lncrlfa'g = I]. Solving this quadratic equation for Ta, we get u u —m1rr§ + motif + ago? [(711.1 — file? + 2 (of — Hg) 111(01fogj] 2_ a
51 fire Td=

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question