1

I wanted to find the outage probability when rate of each user < rate _ threshold over the Rayleigh fading channel. I have found as shown in the following code. However, a research paper uses another equation to find outage probability like 1- exp (2^R-1/ average SNR). Please could you tell me which is the right way :

    `clc; clear variables; close all;

N = 10^5;


d1 = 1000; d2 = 500;    %Distances of users from base station (BS)
a1 = 0.75; a2 = 0.25;   %Power allocation factors
eta = 4;                %Path loss exponent


%Generate rayleigh fading coefficient for both users
h1 = sqrt(d1^-eta)(randn(1,N)+1irandn(1,N))/sqrt(2);
h2 = sqrt(d2^-eta)(randn(1,N)+1irandn(1,N))/sqrt(2);


g1 = (abs(h1)).^2;
g2 = (abs(h2)).^2;


Pt = 0:2:40;                %Transmit power in dBm
pt = (10^-3)10.^(Pt/10);   %Transmit power in linear scale
BW = 10^6;                  %System bandwidth
No = -174 + 10log10(BW);   %Noise power (dBm)
no = (10^-3)*10.^(No/10);   %Noise power (linear scale)


p = length(Pt);
p1 = zeros(1,length(Pt));
p2 = zeros(1,length(Pt));


rate1 = 1; rate2 = 2;       %Target rate of users in bps/Hz
for u = 1:p
    %Calculate SNRs
    gamma_1 = a1pt(u)g1./(a2pt(u)g1+no);
    gamma_12 = a1pt(u)g2./(a2pt(u)g2+no);
    gamma_2 = a2pt(u)g2/no;


%Calculate achievable rates
R1 = log2(1+gamma_1);
R12 = log2(1+gamma_12);
R2 = log2(1+gamma_2);

%Find average of achievable rates
R1_av(u) = mean(R1);
R12_av(u) = mean(R12);
R2_av(u) = mean(R2);

%Check for outage
for k = 1:N
    if R1(k) &lt; rate1
        p1(u) = p1(u)+1;
    end
    if (R12(k) &lt; rate1)||(R2(k) &lt; rate2)
        p2(u) = p2(u)+1;
    end
end



end


pout1 = p1/N; 
pout2 = p2/N;


figure;
semilogy(Pt, pout1, 'linewidth', 1.5); hold on; grid on;
semilogy(Pt, pout2, 'linewidth', 1.5);
xlabel('Transmit power (dBm)');
ylabel('Outage probability');
legend('User 1 (far user)','User 2 (near user)');


figure;
plot(Pt, R1_av, 'linewidth', 1.5); hold on; grid on;
plot(Pt, R12_av, 'linewidth', 1.5);
plot(Pt, R2_av, 'linewidth', 1.5);
xlabel('Transmit power (dBm)');
ylabel('Achievable capacity (bps/Hz)');
legend('R_1','R_{12}','R_2')``
noor
  • 11

0 Answers0