%Problem 4.16;
%verifying small contribution of external MAI in asynchronous cellular cdma
%network; 

clear all; close all;
N=80; K=30; %spreading factor and number of users per cell;
S=(-1).^unidrnd(2,K-1,N); %internal signatures;
maii=sum(S); MI=max(abs(maii)); %internal MAI;
Se=(-1).^unidrnd(2,K*6,N); %external signatures;
Fi=unifrnd(0,2*pi,1,K*6); %random angle polar coordinates of all external mobiles;
Ro=unifrnd(0,1,1,K*6); Ro=sqrt(Ro); %radius polar coordinates of external mobiles, uniform distribution of external mobiles over cell is obtained;
dat=(Ro./sqrt(4+Ro.^2+4*Ro.*cos(Fi))).^1.9; %Okumura-Hata distance attenuation of external signals;
maie=dat*Se; ME=max(abs(maie)); %external mai;
subplot(211); plot([0:79],[maii;maie]); ylim([-1.2 1.2]*(MI+ME)); ylabel('MAI'); xlabel('t'); grid; %plotting internal and external MAI;
legend('ixt.','ext.');
mai=maii+maie; %total mai;
subplot(212); plot([0:79],mai); ylim([-1.2 1.2]*(MI+ME)); ylabel('Total MAI'); grid; xlabel('t'); %plotting total MAI;
Pi=var(maii); Ptot=var(mai); MaiGr=Ptot/Pi; %calculates increase in MAI power;
disp('     Pint     Ptot      Ptot/Pint');
disp([Pi,Ptot,MaiGr]);
x=Ro.*cos(Fi); y=Ro.*sin(Fi); % initializes cartesian coordinates of mobiles with respect to the proper BS;
k=1:6; X=kron(ones(1,K),2*cos((pi*k)/3)); Y=kron(ones(1,K),2*sin((pi*k)/3)); %coordinates of external BSs;
x=X+x; y=Y+y; %coordinates of external mobiles;
figure; scatter(x,y); %plots scatter graph of mobiles;
teta=2*pi*[0:1:99]/100; cirx=cos(teta); ciry=sin(teta);
hold on; axis equal; axis off;
plot(cirx,ciry); plot(0,0,'b^'); %plots internal cell bound and center;
for k=1:6
    circx=cirx+2*cos((pi*k)/3); circy=ciry+2*sin((pi*k)/3);
    plot(circx,circy); %plots external cell bounds;
    plot(2*cos((pi*k)/3),2*sin((pi*k)/3),'r^'); %plots external cells centers
end;