% Author: Chiranjib Saha and Harpreet S. Dhillon

% Main code for "Machine Learning meets Stochastic Geometry:

% Determinantal Subset Selection for Wireless Networks"

% Train the DPP model

%%%%%%%%%%%%%%%%%%%%%

clear all; close all;

addpath(genpath('.\DataSet\'));

parameters;

% load the training data

load TrainingDataSingleClusters;

% Set the size of the training set

T =50;

TrainingCollection = {TrainingDataSet{1:T}};

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

booleOptSigma = 1; % this option enables the parameterization of S

theta = [1,1,1];

sigma = 1;

param = [theta, sigma];

funMax_theta=@(param)funLikelihood_data(T,TrainingCollection,diskradius,choiceKernel,param,alpha);

funMin=@(theta)(-1*funMax_theta(theta)); �fine function to be minimized

% Initial values of the parameters

if choiceKernel==3

thetaGuess = [10,1,1];

else

thetaGuess = [10,1,1,1];

end

options=optimset('Display','iter'); %options for fminsearch

thetaMax=fminunc(funMin,thetaGuess,options); %minimize function

if booleOptSigma

sigma=thetaMax(end); %retrive sigma values from theta

thetaMax=thetaMax(1:end-1);

end

% Display the trained parameters

sigma

thetaMax

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% End of DPP training%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% learn the activation probability

p_a_1= 0;

p_a_2 = 0;

for tt = 1: T

p_a_1 = p_a_1 TrainingCollection{tt}.S_max(1);

p_a_2 = p_a_2 TrainingCollection{tt}.S_max(end);

end

p_a_1 = p_a_1/T;

p_a_2 = p_a_2/T;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Start of Testing %%

load('TrainingDataSingleClustersPart2.mat');

TestSet = TrainingDataSet;

numbSim =size(TestSet,2);

for ss=1:numbSim

% Read the dataset %%

link_distance = TestSet{ss}.link_distance;

tr_loc = TestSet{ss}.tr_loc;

rec_loc = TestSet{ss}.rec_loc;

S_max = TestSet{ss}.S_max;

maxrate = TestSet{ss}.maxrate;

N = size(TestSet{ss}.link_distance,2);

%%%%%%%%%%%%%%%%%%%%%%

Total_power= (link_distance.^(-alpha/2)).^2;

[L,~] = funNeighbourL(Total_power,link_distance,tr_loc,rec_loc,diskradius,choiceKernel,sigma,thetaMax);

S = sample_dpp(decompose_kernel(L));

P_alloc_DPP_sample = 0.01*ones(1,N);

P_alloc_DPP_sample(S) = 1;

SINR = funComputesinr(link_distance,P_alloc_DPP_sample',N0,alpha);

sumrate_Random_DPP(ss) = sum(log2(1 SINR));

S_MAP = greedy_sym(L);

P_alloc_MAP = 0.01*ones(1,N);

P_alloc_MAP(S_MAP) = 1;

SINR = funComputesinr(link_distance,P_alloc_MAP',N0,alpha);

sumrate_MAP(ss) = sum(log2(1 SINR));

S = rand(1,N)<p_a_1;

P_alloc_random = (S==0)*0.01 (S==1)*1;

SINR = funComputesinr(link_distance,P_alloc_random',N0,alpha);

sumrate_random(ss) = sum(log2(1 SINR));

sumrate_opt(ss) = maxrate;

fprintf('\n Sum rate: optimal = %f, DPP = %f, Random = %f',sumrate_opt(ss),sumrate_MAP(ss),sumrate_random(ss));

end

save('rate_compare_data','sumrate_opt','sumrate_MAP','sumrate_random','sumrate_Random_DPP')

% plotting module %

close all

figure(1);

axes1 = axes('Parent',figure(1));

hold(axes1,'on');

[f,x] =ecdf(sumrate_opt);

l_opt = plot(x,f,'-','linewidth',2,'Color',[0.850980392156863 0.325490196078431 0.0980392156862745]);

[f,x] =ecdf(sumrate_MAP);

l_DPP_MAP = plot(x,f,'k--','linewidth',2);

[f,x] =ecdf(sumrate_random);

l_ind = plot(x,f,'linewidth',2,'LineStyle','-.',...

'Color',[0.231372549019608 0.443137254901961 0.337254901960784])

[f,x] = ecdf(sumrate_Random_DPP);

l_DPP_sample = plot(x,f,'r-','linewidth',2);

l =legend([l_opt,l_DPP_MAP,l_DPP_sample,l_ind],'Optimum','DPP (MAP inference)','DPP (Sampling)','Independent Thinning');

set(l,'interpreter','latex','fontsize',16);

xlabel('Sum rate (bps)','interpreter','latex','fontsize',16);

ylabel('CDF','interpreter','latex','fontsize',16);

box on;

grid on;

xlim([8,27])

set(axes1,'FontName','Times New Roman','FontSize',14);