Simple power control in communication systems via GP.

% Boyd, Kim, Vandenberghe, and Hassibi, "A Tutorial on Geometric Programming"
% Written for CVX by Almir Mutapcic 02/08/06
% (a figure is generated)
%
% Solves the power control problem in communication systems, where
% we want to minimize the total transmitter power for n transmitters,
% subject to minimum SINR level, and lower and upper bounds on powers.
% This results in a GP:
%
%   minimize   sum(P)
%       s.t.   Pmin <= P <= Pmax
%              SINR >= SINR_min
%
% where variables are transmitter powers P.
% Numerical data for the specific examples was made up.

% problem constants
n = 5;                 % number of transmitters and receivers
sigma = 0.5*ones(n,1); % noise power at the receiver i
Pmin = 0.1*ones(n,1);  % minimum power at the transmitter i
Pmax = 5*ones(n,1);    % maximum power at the transmitter i
SINR_min = 2;          % threshold SINR for each receiver

% path gain matrix
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];

% variables are power levels
cvx_begin gp
  variable P(n)

  % objective function is the total transmitter power
  minimize( sum(P) )
  subject to

    % formulate the inverse SINR at each receiver using vectorize features
    Gdiag = diag(G);          % the main diagonal of G matrix
    Gtilde = G - diag(Gdiag); % G matrix without the main diagonal
    % inverse SINR
    inverseSINR = (sigma + Gtilde*P)./(Gdiag.*P);

    % constraints are power limits and minimum SINR level
    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
 
Successive approximation method to be employed.
   SDPT3 will be called several times to refine the solution.
   Original size: 91 variables, 29 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
   Approximation size: 300 variables, 159 equality constraints
-----------------------------------------------------------------
 Target     Conic    Solver
Precision   Error    Status
---------------------------
1.221e-04  7.286e-01  Unbounded
1.221e-04  2.125e-02  Solved
1.221e-04  4.797e-05  Solved
1.221e-04  0.000e+00  Solved
1.490e-08  1.895e-08  Solved
1.490e-08  0.000e+00  Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +17.0014

The minimum total transmitter power is 17.00.
Optimal power levels are: 

P =

    3.6601
    3.1623
    2.9867
    4.1647
    3.0276