How Are Expressions Derived from Previous Equations in Mathematical Problems?

skku · Nov 6, 2013

Problem number 1:
How the author has achieved expression 7 and 8 by using 6?

Typeset equations (5) to (8) from a paper on outage probability and SINR thresholds: Pout = Pr(min(γbk, γac) < γthR), R = Bef η log2(1 + γ/γef), γthD = γef(2^(R/(Bef η)) − 1), and γthR = γef(2^(2R/(Bef η)) − 1).

Problem number 2:
How the author has achieved expression 13,14 and 15 by using 12?

Equations (11) to (15) from a paper on relay outage probability: an integral for P_outF, the optimal relay position minimisation, and the outage expansion with CDF terms F and the Rician K factor.

Thanks in advance

mfb · Nov 7, 2013

Just arithmetics. Divide (6) by B*η, put both sides in an exponent (2^...), simplify, rename γ to γ_thD.
To get (8), replace R by 2R.

I think the second problem needs some formulas not given in the image.

How Are Expressions Derived from Previous Equations in Mathematical Problems?

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