mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-18 01:52:05 -05:00
db1454e927
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@8405 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
90 lines
2.6 KiB
Mathematica
90 lines
2.6 KiB
Mathematica
clear all;
|
|
global N
|
|
global R
|
|
global A
|
|
|
|
#-------------------------------------------------------------------------------
|
|
function retval = f1(theta)
|
|
global N;
|
|
global R;
|
|
retval=0.0;
|
|
gterm = gammaln(N/2) - gammaln((N+1)/2) - log(2*sqrt(pi));
|
|
rhs = -N*R*log(2);
|
|
lhs=gterm + (N-1)*log(sin(theta)) + log(1-(tan(theta).^2)/N) - log(cos(theta));
|
|
retval = rhs-real(lhs);
|
|
endfunction
|
|
#-------------------------------------------------------------------------------
|
|
|
|
#-------------------------------------------------------------------------------
|
|
function retval = d(N,i,x)
|
|
t1=(x.^2)/2;
|
|
t2=gammaln(N/2);
|
|
t3=-gammaln(i/2+1);
|
|
t4=-gammaln(N-i);
|
|
t5=(N-1-i)*log(sqrt(2)*x);
|
|
t6=-log(2)/2;
|
|
t7arg=1+(-1)^i * gammainc((x.^2)/2.0,(i+1)/2);
|
|
t7=log(t7arg);
|
|
retval=t1+t2+t3+t4+t5+t6+t7;
|
|
endfunction
|
|
#-------------------------------------------------------------------------------
|
|
|
|
#-------------------------------------------------------------------------------
|
|
function retval = maxstar(x1,x2)
|
|
retval = max(x1,x2)+log(1+exp(-abs(x1-x2)));
|
|
endfunction
|
|
#-------------------------------------------------------------------------------
|
|
|
|
#-------------------------------------------------------------------------------
|
|
function retval = spb_integrand(x)
|
|
global N;
|
|
global A;
|
|
|
|
t1=log(N-1);
|
|
t2=-N*(A^2)/2;
|
|
t3=-0.5*log(2*pi);
|
|
t4=(N-2)*log(sin(x));
|
|
|
|
arg=sqrt(N)*A*cos(x);
|
|
t5=maxstar(d(N,0,arg),d(N,1,arg));
|
|
for i=2:N-1
|
|
t5=maxstar(t5,d(N,i,arg));
|
|
endfor
|
|
|
|
retval=exp(t1+t2+t3+t4+t5);
|
|
endfunction
|
|
#-------------------------------------------------------------------------------
|
|
|
|
#-------------------------------------------------------------------------------
|
|
function retval = qfunc(x)
|
|
retval = 0.5 * erfc(x/sqrt(2));
|
|
endfunction
|
|
#-------------------------------------------------------------------------------
|
|
|
|
#-------------------------------------------------------------------------------
|
|
# Calculate sphere packing lower bound on the probability of word error
|
|
# given block length (N), code rate (R), and Eb/No.
|
|
#
|
|
# Ref:
|
|
# "Log-Domain Calculation of the 1959 Sphere-Packing Bound with Application to
|
|
# M-ary PSK Block Coded Modulation," Igal Sason and Gil Weichman,
|
|
# doi: 10.1109/EEEI.2006.321097
|
|
#-------------------------------------------------------------------------------
|
|
N=174
|
|
K=75
|
|
R=K/N
|
|
|
|
delta=0.01;
|
|
[ths,fval,info,output]=fzero(@f1,[delta,pi/2-delta], optimset ("jacobian", "off"));
|
|
|
|
for ebnodb=-6:0.5:4
|
|
ebno=10^(ebnodb/10.0);
|
|
esno=ebno*R;
|
|
A=sqrt(2*esno);
|
|
term1=quadcc(@spb_integrand,ths,pi/2);
|
|
term2=qfunc(sqrt(N)*A);
|
|
pe=term1+term2;
|
|
ps=1-pe;
|
|
printf("%f %f\n",ebnodb,ps);
|
|
endfor
|