Simple power control in communication systems via GP.
n = 5;
sigma = 0.5*ones(n,1);
Pmin = 0.1*ones(n,1);
Pmax = 5*ones(n,1);
SINR_min = 2;
G = [1.0 0.1 0.2 0.1 0.0
0.1 1.0 0.1 0.1 0.0
0.2 0.1 2.0 0.2 0.2
0.1 0.1 0.2 1.0 0.1
0.0 0.0 0.2 0.1 1.0];
cvx_begin gp
variable P(n)
minimize( sum(P) )
subject to
Gdiag = diag(G);
Gtilde = G - diag(Gdiag);
inverseSINR = (sigma + Gtilde*P)./(Gdiag.*P);
P >= Pmin;
P <= Pmax;
inverseSINR <= (1/SINR_min);
cvx_end
fprintf(1,'\nThe minimum total transmitter power is %3.2f.\n',cvx_optval);
disp('Optimal power levels are: '), P
Calling SeDuMi: 520 variables (10 free), 300 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1 by AdvOL, 2005 and Jos F. Sturm, 1998, 2001-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 10 free variables
eqs m = 300, order n = 231, dim = 831, blocks = 21
nnz(A) = 1016 + 0, nnz(ADA) = 4130, nnz(L) = 2286
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.88E-001 0.000
1 : 5.70E+000 1.79E-001 0.000 0.3674 0.9000 0.9000 2.26 1 1 2.4E+000
2 : 5.14E+000 5.22E-002 0.000 0.2915 0.9000 0.9000 1.71 1 1 5.3E-001
3 : 3.82E+000 1.48E-002 0.000 0.2841 0.9000 0.9000 1.24 1 1 1.4E-001
4 : 3.18E+000 4.58E-003 0.000 0.3089 0.9000 0.9000 1.20 1 1 4.2E-002
5 : 3.04E+000 1.54E-003 0.000 0.3370 0.9000 0.9000 1.30 1 1 1.2E-002
6 : 2.96E+000 9.15E-004 0.000 0.5923 0.9000 0.9000 1.32 1 1 6.7E-003
7 : 2.87E+000 2.52E-004 0.000 0.2757 0.9000 0.9000 1.13 1 1 1.8E-003
8 : 2.84E+000 1.79E-005 0.000 0.0710 0.9900 0.9900 1.09 1 1 1.2E-004
9 : 2.83E+000 4.65E-007 0.000 0.0260 0.9900 0.9900 1.08 1 1 2.9E-006
10 : 2.83E+000 8.86E-008 0.000 0.1908 0.9000 0.9000 1.01 1 2 5.5E-007
11 : 2.83E+000 8.36E-009 0.189 0.0943 0.9900 0.9900 1.00 2 3 5.2E-008
12 : 2.83E+000 1.41E-010 0.000 0.0169 0.9000 0.0000 1.00 4 7 1.8E-008
13 : 2.83E+000 2.66E-011 0.000 0.1884 0.9089 0.9000 1.00 11 12 3.5E-009
iter seconds digits c*x b*y
13 0.2 Inf 2.8338047822e+000 2.8338050242e+000
|Ax-b| = 1.3e-008, [Ay-c]_+ = 2.5E-009, |x|= 2.8e+001, |y|= 6.4e+000
Detailed timing (sec)
Pre IPM Post
0.000E+000 1.903E-001 0.000E+000
Max-norms: ||b||=4.380570e+000, ||c|| = 2.202759e+000,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 19.5702.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +17.0101
The minimum total transmitter power is 17.01.
Optimal power levels are:
P =
3.6613
3.1633
2.9882
4.1666
3.0291