N = 32e9;
M = 3;
eps = 1e-4;

delta_1 = 24 * sqrt((M-1)/N) * log(M*N) * (2*sqrt(log(M * N) - log(eps)) + 1);
delta_2 = 3/2 * sqrt((M-1)/N) * (2*sqrt(log(M * 2) - log(eps)) + 1);

K = N * (1/8 - delta_1 - delta_2)^2 / (81 * M * log(M * N) * (1 + 2/3 * delta_2));

x = 0:25;
Ns = N * (1+randn(size(x)));
delta_1 = 24 * sqrt((M-1)./N) * log(M.*N) * (2*sqrt(log(M .* N) - log(eps)) + 1);
delta_2 = 3/2 * sqrt((M-1)./N) * (2*sqrt(log(M * 2) - log(eps)) + 1);
Ks = Ns * (1/8 - delta_1 - delta_2)^2 / (81 * M * log(M .* Ns) * (1 + 2/3 * delta_2));

rate = K .* M .* log(M .* Ns) ./ Ns;
plot(x, rate)