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hw4_new_soln

# hw4_new_soln - EE 359 Wireless Communications Fall 2009...

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EE 359 - Wireless Communications - Fall 2009 Homework 4 Solutions 1. (4-8) (10pts) (a) (4pts) If neither transmitter nor receiver knows when the interferer is on, they must transmit assuming worst case, i.e. as if the interferer was on all the time, C = B log ( 1 + S N 0 B + I ) = 10 . 7 Kbps. (b) (4pts) Suppose we transmit at power S 1 when jammer is off and S 2 when jammer is off, C = B max [ log ( 1 + S 1 N o B ) 0 . 75 + log ( 1 + S 2 N o B + I ) 0 . 25 ] subject to 0 . 75 S 1 + 0 . 25 S 2 = S. This gives S 1 = 12 . 25 mW , S 2 = 3 . 25 mW and C = 53 . 21 Kbps . (c) (2pts) The jammer should transmit x ( t ) to completely cancel off the signal. 2. (4-13) (20pts) (a) (10pts) C=13.98Mbps MATLAB Gammabar = [1 .5 .125]; ss = .001; P = 30e-3; N0 = .001e-6; Bc = 4e6; Pnoise = N0*Bc; hsquare = [ss:ss:10*max(Gammabar)]; gamma = hsquare*(P/Pnoise); for i = 1:length(Gammabar) pgamma(i,:) = (1/Gammabar(i))*exp(-hsquare/Gammabar(i)); end gamma0v = [1:.01:2]; for j = 1:length(gamma0v) gamma0 = gamma0v(j); sumP(j) = 0; for i = 1:length(Gammabar) a = gamma.*(gamma>gamma0); [b,c] = max(a>0); gammac = a(find(a)); pgammac = pgamma(i,c:length(gamma));

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Pj_by_P = (1/gamma0)-(1./gammac); sumP(j) = sumP(j) + sum(Pj_by_P.*pgammac)*ss; end end [b,c] = min(abs((sumP-1))); gamma0ch = gamma0v(c); C = 0; for i = 1:length(Gammabar) a = gamma.*(gamma>gamma0ch); [b,c] = max(a>0); gammac = a(find(a)); pgammac = pgamma(i,c:length(gamma)); C = C + Bc*ss*sum(log2(gammac/gamma0ch).*pgammac); end (b) (10pts) C=13.27Mbps MATLAB Gammabarv = [1 .5 .125]; ss = .001; Pt = 30e-3; N0 = .001e-6;
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