├── LICENSE ├── README.md ├── cal_kl11.m ├── capa_cal.m ├── capacity_K.m ├── capacity_N.m ├── capacity_Pro.m ├── capacity_R.m ├── capacity_SNR.m ├── greedy_appr.m ├── maxmi_appr.m ├── pf_appr.m └── proposed.m /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Beam-grouping-based-user-scheduling-in-multi-cell-millimeter-wave-MIMO-systems 2 | This repository is about the paper and the code of "Beam grouping based user scheduling in multi-cell millimeter-wave MIMO systems". 3 | 4 | Recommended citation: 'A. Hu, "Beam grouping based user scheduling in multi-cell millimeter-wave MIMO systems,"IEEE Access, vol. 6, 5 | pp. 55004-55012, Oct. 2018.' 6 | -------------------------------------------------------------------------------- /cal_kl11.m: -------------------------------------------------------------------------------- 1 | flag_kl1 = 0; 2 | if 1==lll1 3 | else 4 | for kc_c = 1 : Nr 5 | for ll_c = 1 : L 6 | if ll_c==l1 7 | else 8 | if K_ind(kc_c, ll_c) > 0 9 | [~,ps] = max(beta_store(K_ind(kc_c, ll_c), (ll_c-1)*P+1:ll_c*P)); 10 | nx = floor((cos(thetab_store(K_ind(kc_c, ll_c), (ll_c-1)*P+ps)) * sin(phib_store(K_ind(kc_c, ll_c), (ll_c-1)*P+ps))+1)*naz*0.5); 11 | ny = floor((sin(thetab_store(K_ind(kc_c, ll_c), (ll_c-1)*P+ps))+1)*nel*0.5); 12 | nn = ny; 13 | nnn=nx; 14 | if block_store(k, (ll_c-1)*L+l1)>0 15 | else 16 | pp_c=1; 17 | nx = floor((cos(thetabb_store(k, (ll_c-1)*L*P+(l1-1)*P+pp_c)) * sin(phibb_store(k, (ll_c-1)*L*P+(l1-1)*P+pp_c))+1)*naz*0.5); 18 | ny = floor((sin(thetabb_store(k, (ll_c-1)*L*P+(l1-1)*P+pp_c))+1)*nel*0.5); 19 | nn_c = ny; 20 | nnn_c = nx; 21 | if abs(nn_c-nn)+abs(nnn_c-nnn)<4 22 | flag_kl1 = 1; 23 | break; 24 | else 25 | end 26 | end 27 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 28 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 29 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 30 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 31 | nn = ny; 32 | nnn=nx; 33 | if block_store(K_ind(kc_c, ll_c), (l1-1)*L+ll_c)>0 34 | else 35 | pp_c=1; 36 | nx = floor((cos(thetabb_store(K_ind(kc_c, ll_c), (l1-1)*L*P+(ll_c-1)*P+pp_c)) * sin(phibb_store(K_ind(kc_c, ll_c), (l1-1)*L*P+(ll_c-1)*P+pp_c))+1)*naz*0.5); 37 | ny = floor((sin(thetabb_store(K_ind(kc_c, ll_c), (l1-1)*L*P+(ll_c-1)*P+pp_c))+1)*nel*0.5); 38 | nn_c = ny; 39 | nnn_c = nx; 40 | if abs(nn_c-nn)+abs(nnn_c-nnn)<4 41 | flag_kl1 = 1; 42 | break; 43 | else 44 | end 45 | end 46 | else 47 | end 48 | end 49 | end 50 | end 51 | end -------------------------------------------------------------------------------- /capa_cal.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 2 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 3 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 4 | %%%capacity calculation%%%%%%%%%%%%%%% 5 | capacity_temp_in = zeros(K,L); 6 | for l1 = 1 : L%j, user cell 7 | nre=sum(C_sel(:, l1)); 8 | if 0 == nre 9 | continue; 10 | else 11 | end 12 | for kc = 1 : nre 13 | k = K_ind(kc, l1);%%%%k 14 | if 1==kc 15 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 16 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 17 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 18 | nn = ny * maz + nx + 1; 19 | wj = Um(:,nn); 20 | else 21 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 22 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 23 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 24 | nn = ny * maz + nx + 1; 25 | wj_temp = [wj,Um(:,nn)]; 26 | wj = wj_temp; 27 | end 28 | end 29 | interfandnoise = zeros(nre, 1); 30 | for l2 = 1 : L%%%l, bs cell 31 | nrel2=sum(C_sel(:, l2)); 32 | if l2==l1 || 0== nrel2 33 | continue; 34 | else 35 | for kc = 1 : nrel2 36 | k = K_ind(kc, l2); 37 | if 1==kc 38 | [~,ps] = max(beta_store(k, (l2-1)*P+1:l2*P)); 39 | nx = floor((cos(thetab_store(k, (l2-1)*P+ps)) * sin(phib_store(k, (l2-1)*P+ps))+1)*naz*0.5); 40 | ny = floor((sin(thetab_store(k, (l2-1)*P+ps))+1)*nel*0.5); 41 | nn = ny * naz + nx + 1; 42 | Ul = U(:, nn); 43 | else 44 | [~,ps] = max(beta_store(k, (l2-1)*P+1:l2*P)); 45 | nx = floor((cos(thetab_store(k, (l2-1)*P+ps)) * sin(phib_store(k, (l2-1)*P+ps))+1)*naz*0.5); 46 | ny = floor((sin(thetab_store(k, (l2-1)*P+ps))+1)*nel*0.5); 47 | nn = ny * naz + nx + 1; 48 | Ul_temp = [Ul,U(:, nn)]; 49 | Ul = Ul_temp; 50 | end 51 | end 52 | Zjl = zeros(nre, nrel2); 53 | for kkk = 1 : nre 54 | k = K_ind(kkk, l1);%%%%k 55 | Zjl(kkk, :) = wj(:,kkk)' * H(:,(l2-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l2-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul; 56 | end 57 | switch l2 58 | case 1 59 | Zll = Zjj_1; 60 | case 2 61 | Zll = Zjj_2; 62 | case 3 63 | Zll = Zjj_3; 64 | otherwise 65 | end 66 | X = inv(Zll) * (inv(Zll))'; 67 | for kc = 1 : nre 68 | interfandnoise(kc, 1) = interfandnoise(kc, 1) + (norm(Zjl(kc, :)/ Zll))^2 / trace(X); 69 | end 70 | end 71 | end 72 | interfandnoise = interfandnoise + 1/Pvsigma2; 73 | switch l1 74 | case 1 75 | Zjj = Zjj_1; 76 | case 2 77 | Zjj = Zjj_2; 78 | case 3 79 | Zjj = Zjj_3; 80 | otherwise 81 | end 82 | anotherf = trace(inv(Zjj) * (inv(Zjj))'); 83 | for kc = 1 : nre 84 | k = K_ind(kc, l1); 85 | capacity_temp_in(k, l1) = log2(1+1 / abs(anotherf * interfandnoise(kc, 1))); 86 | end 87 | end -------------------------------------------------------------------------------- /capacity_K.m: -------------------------------------------------------------------------------- 1 | clear; 2 | close all; 3 | L = 3; 4 | naz = 12; 5 | nel = 100; 6 | n_arr = naz * nel; 7 | maz = 2; 8 | mel = 2; 9 | m_arr = maz * mel; 10 | Rmin = 90; 11 | Rmax = 100; 12 | base = [0, 0; 0, 2 * Rmax; sqrt(3) * Rmax, Rmax;]; 13 | Nr = 4; 14 | P = 4; 15 | K = 20; 16 | variable_s = [10; 20; 30; 40; 50;]; 17 | Pvsigma2 = 1e18; 18 | height = 10; 19 | time_fre_resources = 20; 20 | f = 80*10^9;%1G bandwidth 21 | lambda = 3 * 10^8 / f; 22 | miu = 0.5; 23 | beta_m = 10.3 * pi / 180; 24 | Nite = 1e4; 25 | capacity = zeros(length(variable_s), 6); 26 | jain = zeros(length(variable_s), 6); 27 | angle = zeros(1, 2); 28 | U = zeros(n_arr, n_arr); 29 | for nx = 0 : naz-1 30 | for ny = 0 : nel-1 31 | angle(1, 2) = (-1+2*ny/nel);%el 32 | angle(1, 1) = (-1+2*nx/naz);%az 33 | n = ny * naz + nx + 1; 34 | for mx = 0 : naz-1 35 | for my = 0 : nel-1 36 | m = my * naz + 1 + mx; 37 | U(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(naz-1)) * angle(1, 1) + (my-0.5*(nel-1)) * angle(1, 2))) / sqrt(n_arr); 38 | end 39 | end 40 | end 41 | end 42 | Um = zeros(m_arr, m_arr); 43 | for nx = 0 : maz-1 44 | for ny = 0 : mel-1 45 | angle(1, 2) = (-1+2*ny/mel);%el 46 | angle(1, 1) = (-1+2*nx/maz);%az 47 | n = ny * maz + nx + 1; 48 | for mx = 0 : maz-1 49 | for my = 0 : mel-1 50 | m = my * maz + 1 + mx; 51 | Um(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(maz-1)) * angle(1, 1) + (my-0.5*(mel-1)) * angle(1, 2))) / sqrt(m_arr); 52 | end 53 | end 54 | end 55 | end 56 | for variable_n = 1 : length(variable_s) 57 | K = variable_s(variable_n, 1); 58 | for ii = 1 : Nite 59 | H = zeros(m_arr, K*L*L*n_arr); 60 | p_store = zeros(K, L); 61 | beta_store = zeros(K, P*L); 62 | betab_store = zeros(K, P*L*L); 63 | thetab_store = zeros(K, P*L); 64 | thetabb_store = zeros(K, P*L*L); 65 | phib_store = zeros(K, P*L); 66 | phibb_store = zeros(K, P*L*L); 67 | thetam_store = zeros(K, P*L); 68 | phim_store = zeros(K, P*L); 69 | pos_store = zeros(K*L, 2); 70 | for l = 1 : L 71 | for k = 1 : K 72 | pos_temp = zeros(1, 2); 73 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 74 | pos_temp(1, 1) = rand(1, 1) * Rmax; 75 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 76 | end 77 | switch l 78 | case 1 79 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 80 | case 2 81 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 82 | case 3 83 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 84 | otherwise 85 | end 86 | d_temp = norm(pos_temp); 87 | pos_temp(1, 1) = d_temp * cos(angle_temp); 88 | pos_temp(1, 2) = d_temp * sin(angle_temp); 89 | pos_store((l-1)*K+k, :) = pos_temp;%relative to the serving BS 90 | end 91 | end 92 | pos = zeros(K, 3); 93 | theta = zeros(K, P); 94 | phi = zeros(K, P); 95 | beta = zeros(K, P); 96 | theta_m = zeros(K, P); 97 | phi_m = zeros(K, P); 98 | block_store = zeros(K, L*L); 99 | for l1 = 1 : L 100 | for l2 = 1 : L 101 | for k = 1 : K 102 | for p = 1 : P 103 | if 1==p 104 | pos_temp = pos_store((l2-1)*K+k, :) + base(l2, :)-base(l1, :);%%relative position of MS in the l2-th cell to l1-th BS 105 | pos(k, 3) = norm(pos_temp); 106 | pos(k, 3) = norm([pos(k, 3), height]);%distance 107 | if rand(1,1)>0.1 108 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 109 | switch l1 110 | case 1 111 | phi(k, p) = phi(k, p) - pi / 3;%az 112 | case 2 113 | phi(k, p) = phi(k, p) + pi / 3;%az 114 | case 3 115 | phi(k, p) = phi(k, p) - pi;%az 116 | otherwise 117 | end 118 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 119 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 120 | phi_m(k, p) = pi - phi(k, p); 121 | theta_m(k, p) = pi - theta(k, p); 122 | else 123 | block_store(k, (l1-1)*L+l2) = 1; 124 | beta(k, p) = 0; 125 | continue; 126 | end 127 | else 128 | %take the reflector inside the cell 129 | pos_temp = zeros(1, 2); 130 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 131 | pos_temp(1, 1) = rand(1, 1) * Rmax; 132 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 133 | end 134 | switch l2 135 | case 1 136 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 137 | case 2 138 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 139 | case 3 140 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 141 | otherwise 142 | end 143 | d_temp = norm(pos_temp); 144 | pos_temp(1, 1) = d_temp * cos(angle_temp); 145 | pos_temp(1, 2) = d_temp * sin(angle_temp); 146 | pos_temp = pos_temp + base(l2, :)-base(l1, :); 147 | pos(k, 3) = norm(pos_temp); 148 | pos(k, 3) = norm([pos(k, 3), height]);%distance 149 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 150 | switch l1 151 | case 1 152 | phi(k, p) = phi(k, p) - pi / 3;%az 153 | case 2 154 | phi(k, p) = phi(k, p) + pi / 3;%az 155 | case 3 156 | phi(k, p) = phi(k, p) - pi;%az 157 | otherwise 158 | end 159 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 160 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 161 | phi_m(k, p) = pi - phi(k, p); 162 | theta_m(k, p) = pi - theta(k, p); 163 | end 164 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 165 | Aaz = -min(12 * phi(k, p)^2 / (70/180*pi)^2, 25); 166 | Ael = -min(12 * theta(k, p)^2 / (7/180*pi)^2, 20); 167 | D0 = -min(-Aaz-Ael, 25); 168 | D0 = 10^(D0*0.1); 169 | if p < 2 170 | if block_store(k, (l1-1)*L+l2) > 0 171 | else 172 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi); 173 | end 174 | else 175 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi) * 10^((-rand(1,1) * 5 - 15)*0.05);%-15~-20dB loss 176 | end 177 | hb = zeros(n_arr, 1); 178 | for nx = 0 : naz-1 179 | for ny = 0 : nel-1 180 | n = ny * naz+ 1 + nx; 181 | hb(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(naz-1)) * cos(theta(k, p)) * sin(phi(k, p)) + (ny-0.5*(nel-1)) * sin(theta(k, p)))); 182 | end 183 | end 184 | hm = zeros(m_arr, 1); 185 | for nx = 0 : maz-1 186 | for ny = 0 : mel-1 187 | n = ny * maz+ 1 + nx; 188 | hm(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(maz-1)) * cos(theta_m(k, p)) * sin(phi_m(k, p)) + (ny-0.5*(mel-1)) * sin(theta_m(k, p)))); 189 | end 190 | end 191 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) = ... 192 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) + beta(k, p) * hm * hb'; 193 | thetabb_store(k, (l1-1)*L*P+(l2-1)*P+p) = theta(k, p); 194 | phibb_store(k, (l1-1)*L*P+(l2-1)*P+p) = phi(k, p); 195 | betab_store(k, (l1-1)*L*P+(l2-1)*P+p) = abs(beta(k, p)); 196 | if l1==l2 197 | thetab_store(k, (l1-1)*P+p) = theta(k, p); 198 | phib_store(k, (l1-1)*P+p) = phi(k, p); 199 | thetam_store(k, (l1-1)*P+p) = theta_m(k, p); 200 | phim_store(k, (l1-1)*P+p) = phi_m(k, p); 201 | beta_store(k, (l1-1)*P+p) = abs(beta(k, p)); 202 | else 203 | end 204 | end 205 | end 206 | end 207 | end 208 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 209 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 210 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 211 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 212 | greedy_appr;%1 213 | maxmi_appr;%2 214 | pf_appr;%3 215 | proposed;%4-6 216 | disp([variable_n, ii]) 217 | end 218 | end 219 | capacity = capacity / Nite; 220 | jain = jain / Nite; 221 | %%%%%%%%%%%%%%%%%%%%%%%%%%%% 222 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 223 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 224 | 225 | h1 = subplot(1,2,1); 226 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 227 | plot(variable_s, capacity(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 228 | hold on 229 | plot(variable_s, capacity(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 230 | plot(variable_s, capacity(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 231 | plot(variable_s, capacity(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 232 | xlim([min(variable_s), max(variable_s)]) 233 | le = legend('Greedy','Max-min','PF','Proposed', 'Location', 'northwest'); 234 | set(le,'Fontname','Times') 235 | set(gca,'XTick',variable_s) 236 | xlabel('Number of MSs','Fontname','Times') 237 | ylabel('Sum rate (bps/Hz)','Fontname','Times') 238 | grid on%%%%%%%%%%%%%%%%%%%%%%%% 239 | h2 = subplot(1,2,2); 240 | plot(variable_s, jain(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 241 | hold on 242 | plot(variable_s, jain(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 243 | plot(variable_s, jain(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 244 | plot(variable_s, jain(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 245 | xlim([min(variable_s), max(variable_s)]) 246 | set(le,'Fontname','Times') 247 | set(gca,'XTick',variable_s) 248 | xlabel('Number of MSs','Fontname','Times') 249 | ylabel('Jain''s fairness index','Fontname','Times') 250 | grid on -------------------------------------------------------------------------------- /capacity_N.m: -------------------------------------------------------------------------------- 1 | clear; 2 | close all; 3 | L = 3; 4 | naz = 12; 5 | nel = 100; 6 | n_arr = naz * nel; 7 | maz = 2; 8 | mel = 2; 9 | m_arr = maz * mel; 10 | Rmin = 90; 11 | Rmax = 100; 12 | base = [0, 0; 0, 2 * Rmax; sqrt(3) * Rmax, Rmax;]; 13 | Nr = 4; 14 | P = 4; 15 | K = 20; 16 | variable_s1 = [2;5;6;10;12]; 17 | variable_s2 = [20;40;60;80;100]; 18 | variable_s = variable_s1.*variable_s2; 19 | Pvsigma2 = 1e18; 20 | height = 10; 21 | time_fre_resources = 20; 22 | f = 80*10^9;%1G bandwidth 23 | lambda = 3 * 10^8 / f; 24 | miu = 0.5; 25 | beta_m = 10.3 * pi / 180; 26 | Nite = 1e4; 27 | capacity = zeros(length(variable_s), 6); 28 | jain = zeros(length(variable_s), 6); 29 | angle = zeros(1, 2); 30 | for variable_n = 1 : length(variable_s) 31 | n_arr = variable_s(variable_n, 1); 32 | nel = variable_s2(variable_n, 1); 33 | naz = variable_s1(variable_n, 1); 34 | U = zeros(n_arr, n_arr); 35 | for nx = 0 : naz-1 36 | for ny = 0 : nel-1 37 | angle(1, 2) = (-1+2*ny/nel);%el 38 | angle(1, 1) = (-1+2*nx/naz);%az 39 | n = ny * naz + nx + 1; 40 | for mx = 0 : naz-1 41 | for my = 0 : nel-1 42 | m = my * naz + 1 + mx; 43 | U(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(naz-1)) * angle(1, 1) + (my-0.5*(nel-1)) * angle(1, 2))) / sqrt(n_arr); 44 | end 45 | end 46 | end 47 | end 48 | Um = zeros(m_arr, m_arr); 49 | for nx = 0 : maz-1 50 | for ny = 0 : mel-1 51 | angle(1, 2) = (-1+2*ny/mel);%el 52 | angle(1, 1) = (-1+2*nx/maz);%az 53 | n = ny * maz + nx + 1; 54 | for mx = 0 : maz-1 55 | for my = 0 : mel-1 56 | m = my * maz + 1 + mx; 57 | Um(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(maz-1)) * angle(1, 1) + (my-0.5*(mel-1)) * angle(1, 2))) / sqrt(m_arr); 58 | end 59 | end 60 | end 61 | end 62 | for ii = 1 : Nite 63 | H = zeros(m_arr, K*L*L*n_arr); 64 | p_store = zeros(K, L); 65 | beta_store = zeros(K, P*L); 66 | betab_store = zeros(K, P*L*L); 67 | thetab_store = zeros(K, P*L); 68 | thetabb_store = zeros(K, P*L*L); 69 | phib_store = zeros(K, P*L); 70 | phibb_store = zeros(K, P*L*L); 71 | thetam_store = zeros(K, P*L); 72 | phim_store = zeros(K, P*L); 73 | pos_store = zeros(K*L, 2); 74 | for l = 1 : L 75 | for k = 1 : K 76 | pos_temp = zeros(1, 2); 77 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 78 | pos_temp(1, 1) = rand(1, 1) * Rmax; 79 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 80 | end 81 | switch l 82 | case 1 83 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 84 | case 2 85 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 86 | case 3 87 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 88 | otherwise 89 | end 90 | d_temp = norm(pos_temp); 91 | pos_temp(1, 1) = d_temp * cos(angle_temp); 92 | pos_temp(1, 2) = d_temp * sin(angle_temp); 93 | pos_store((l-1)*K+k, :) = pos_temp;%relative to the serving BS 94 | end 95 | end 96 | pos = zeros(K, 3); 97 | theta = zeros(K, P); 98 | phi = zeros(K, P); 99 | beta = zeros(K, P); 100 | theta_m = zeros(K, P); 101 | phi_m = zeros(K, P); 102 | block_store = zeros(K, L*L); 103 | for l1 = 1 : L 104 | for l2 = 1 : L 105 | for k = 1 : K 106 | for p = 1 : P 107 | if 1==p 108 | pos_temp = pos_store((l2-1)*K+k, :) + base(l2, :)-base(l1, :);%%relative position of MS in the l2-th cell to l1-th BS 109 | pos(k, 3) = norm(pos_temp); 110 | pos(k, 3) = norm([pos(k, 3), height]);%distance 111 | if rand(1,1)>0.1 112 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 113 | switch l1 114 | case 1 115 | phi(k, p) = phi(k, p) - pi / 3;%az 116 | case 2 117 | phi(k, p) = phi(k, p) + pi / 3;%az 118 | case 3 119 | phi(k, p) = phi(k, p) - pi;%az 120 | otherwise 121 | end 122 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 123 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 124 | phi_m(k, p) = pi - phi(k, p); 125 | theta_m(k, p) = pi - theta(k, p); 126 | else 127 | block_store(k, (l1-1)*L+l2) = 1; 128 | beta(k, p) = 0; 129 | continue; 130 | end 131 | else 132 | %take the reflector inside the cell 133 | pos_temp = zeros(1, 2); 134 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 135 | pos_temp(1, 1) = rand(1, 1) * Rmax; 136 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 137 | end 138 | switch l2 139 | case 1 140 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 141 | case 2 142 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 143 | case 3 144 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 145 | otherwise 146 | end 147 | d_temp = norm(pos_temp); 148 | pos_temp(1, 1) = d_temp * cos(angle_temp); 149 | pos_temp(1, 2) = d_temp * sin(angle_temp); 150 | pos_temp = pos_temp + base(l2, :)-base(l1, :); 151 | pos(k, 3) = norm(pos_temp); 152 | pos(k, 3) = norm([pos(k, 3), height]);%distance 153 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 154 | switch l1 155 | case 1 156 | phi(k, p) = phi(k, p) - pi / 3;%az 157 | case 2 158 | phi(k, p) = phi(k, p) + pi / 3;%az 159 | case 3 160 | phi(k, p) = phi(k, p) - pi;%az 161 | otherwise 162 | end 163 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 164 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 165 | phi_m(k, p) = pi - phi(k, p); 166 | theta_m(k, p) = pi - theta(k, p); 167 | end 168 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 169 | Aaz = -min(12 * phi(k, p)^2 / (70/180*pi)^2, 25); 170 | Ael = -min(12 * theta(k, p)^2 / (7/180*pi)^2, 20); 171 | D0 = -min(-Aaz-Ael, 25); 172 | D0 = 10^(D0*0.1); 173 | if p < 2 174 | if block_store(k, (l1-1)*L+l2) > 0 175 | else 176 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi); 177 | end 178 | else 179 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi) * 10^((-rand(1,1) * 5 - 15)*0.05);%-15~-20dB loss 180 | end 181 | hb = zeros(n_arr, 1); 182 | for nx = 0 : naz-1 183 | for ny = 0 : nel-1 184 | n = ny * naz+ 1 + nx; 185 | hb(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(naz-1)) * cos(theta(k, p)) * sin(phi(k, p)) + (ny-0.5*(nel-1)) * sin(theta(k, p)))); 186 | end 187 | end 188 | hm = zeros(m_arr, 1); 189 | for nx = 0 : maz-1 190 | for ny = 0 : mel-1 191 | n = ny * maz+ 1 + nx; 192 | hm(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(maz-1)) * cos(theta_m(k, p)) * sin(phi_m(k, p)) + (ny-0.5*(mel-1)) * sin(theta_m(k, p)))); 193 | end 194 | end 195 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) = ... 196 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) + beta(k, p) * hm * hb'; 197 | thetabb_store(k, (l1-1)*L*P+(l2-1)*P+p) = theta(k, p); 198 | phibb_store(k, (l1-1)*L*P+(l2-1)*P+p) = phi(k, p); 199 | betab_store(k, (l1-1)*L*P+(l2-1)*P+p) = abs(beta(k, p)); 200 | if l1==l2 201 | thetab_store(k, (l1-1)*P+p) = theta(k, p); 202 | phib_store(k, (l1-1)*P+p) = phi(k, p); 203 | thetam_store(k, (l1-1)*P+p) = theta_m(k, p); 204 | phim_store(k, (l1-1)*P+p) = phi_m(k, p); 205 | beta_store(k, (l1-1)*P+p) = abs(beta(k, p)); 206 | else 207 | end 208 | end 209 | end 210 | end 211 | end 212 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 213 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 214 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 215 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 216 | greedy_appr;%1 217 | maxmi_appr;%2 218 | pf_appr;%3 219 | proposed;%4-6 220 | disp([variable_n, ii]) 221 | end 222 | end 223 | capacity = capacity / Nite; 224 | jain = jain / Nite; 225 | %%%%%%%%%%%%%%%%%%%%%%%%%%%% 226 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 227 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 228 | 229 | h1 = subplot(1,2,1); 230 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 231 | plot(variable_s, capacity(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 232 | hold on 233 | plot(variable_s, capacity(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 234 | plot(variable_s, capacity(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 235 | plot(variable_s, capacity(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 236 | xlim([min(variable_s), max(variable_s)]) 237 | le = legend('Greedy','Max-min','PF','Proposed', 'Location', 'northwest'); 238 | set(le,'Fontname','Times') 239 | set(gca,'XTick',variable_s) 240 | xlabel('Number of BS antennas','Fontname','Times') 241 | ylabel('Sum rate (bps/Hz)','Fontname','Times') 242 | grid on%%%%%%%%%%%%%%%%%%%%%%%% 243 | h2 = subplot(1,2,2); 244 | plot(variable_s, jain(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 245 | hold on 246 | plot(variable_s, jain(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 247 | plot(variable_s, jain(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 248 | plot(variable_s, jain(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 249 | xlim([min(variable_s), max(variable_s)]) 250 | set(le,'Fontname','Times') 251 | set(gca,'XTick',variable_s) 252 | xlabel('Number of BS antennas','Fontname','Times') 253 | ylabel('Jain''s fairness index','Fontname','Times') 254 | grid on -------------------------------------------------------------------------------- /capacity_Pro.m: -------------------------------------------------------------------------------- 1 | clear; 2 | close all; 3 | L = 3; 4 | naz = 12; 5 | nel = 100; 6 | n_arr = naz * nel; 7 | maz = 2; 8 | mel = 2; 9 | m_arr = maz * mel; 10 | Rmin = 90; 11 | Rmax = 100; 12 | base = [0, 0; 0, 2 * Rmax; sqrt(3) * Rmax, Rmax;]; 13 | Nr = 4; 14 | P = 4; 15 | K = 20; 16 | variable_s = [0; 0.1; 0.2; 0.3; 0.4;]; 17 | Pvsigma2 = 1e18; 18 | height = 10; 19 | time_fre_resources = 20; 20 | f = 80*10^9;%1G bandwidth 21 | lambda = 3 * 10^8 / f; 22 | miu = 0.5; 23 | beta_m = 10.3 * pi / 180; 24 | Nite = 1e4; 25 | capacity = zeros(length(variable_s), 6); 26 | jain = zeros(length(variable_s), 6); 27 | angle = zeros(1, 2); 28 | U = zeros(n_arr, n_arr); 29 | for nx = 0 : naz-1 30 | for ny = 0 : nel-1 31 | angle(1, 2) = (-1+2*ny/nel);%el 32 | angle(1, 1) = (-1+2*nx/naz);%az 33 | n = ny * naz + nx + 1; 34 | for mx = 0 : naz-1 35 | for my = 0 : nel-1 36 | m = my * naz + 1 + mx; 37 | U(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(naz-1)) * angle(1, 1) + (my-0.5*(nel-1)) * angle(1, 2))) / sqrt(n_arr); 38 | end 39 | end 40 | end 41 | end 42 | Um = zeros(m_arr, m_arr); 43 | for nx = 0 : maz-1 44 | for ny = 0 : mel-1 45 | angle(1, 2) = (-1+2*ny/mel);%el 46 | angle(1, 1) = (-1+2*nx/maz);%az 47 | n = ny * maz + nx + 1; 48 | for mx = 0 : maz-1 49 | for my = 0 : mel-1 50 | m = my * maz + 1 + mx; 51 | Um(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(maz-1)) * angle(1, 1) + (my-0.5*(mel-1)) * angle(1, 2))) / sqrt(m_arr); 52 | end 53 | end 54 | end 55 | end 56 | for variable_n = 1 : length(variable_s) 57 | block_pro = variable_s(variable_n, 1); 58 | for ii = 1 : Nite 59 | H = zeros(m_arr, K*L*L*n_arr); 60 | p_store = zeros(K, L); 61 | beta_store = zeros(K, P*L); 62 | betab_store = zeros(K, P*L*L); 63 | thetab_store = zeros(K, P*L); 64 | thetabb_store = zeros(K, P*L*L); 65 | phib_store = zeros(K, P*L); 66 | phibb_store = zeros(K, P*L*L); 67 | thetam_store = zeros(K, P*L); 68 | phim_store = zeros(K, P*L); 69 | pos_store = zeros(K*L, 2); 70 | for l = 1 : L 71 | for k = 1 : K 72 | pos_temp = zeros(1, 2); 73 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 74 | pos_temp(1, 1) = rand(1, 1) * Rmax; 75 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 76 | end 77 | switch l 78 | case 1 79 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 80 | case 2 81 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 82 | case 3 83 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 84 | otherwise 85 | end 86 | d_temp = norm(pos_temp); 87 | pos_temp(1, 1) = d_temp * cos(angle_temp); 88 | pos_temp(1, 2) = d_temp * sin(angle_temp); 89 | pos_store((l-1)*K+k, :) = pos_temp;%relative to the serving BS 90 | end 91 | end 92 | pos = zeros(K, 3); 93 | theta = zeros(K, P); 94 | phi = zeros(K, P); 95 | beta = zeros(K, P); 96 | theta_m = zeros(K, P); 97 | phi_m = zeros(K, P); 98 | block_store = zeros(K, L*L); 99 | for l1 = 1 : L 100 | for l2 = 1 : L 101 | for k = 1 : K 102 | for p = 1 : P 103 | if 1==p 104 | pos_temp = pos_store((l2-1)*K+k, :) + base(l2, :)-base(l1, :);%%relative position of MS in the l2-th cell to l1-th BS 105 | pos(k, 3) = norm(pos_temp); 106 | pos(k, 3) = norm([pos(k, 3), height]);%distance 107 | if rand(1,1)>block_pro 108 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 109 | switch l1 110 | case 1 111 | phi(k, p) = phi(k, p) - pi / 3;%az 112 | case 2 113 | phi(k, p) = phi(k, p) + pi / 3;%az 114 | case 3 115 | phi(k, p) = phi(k, p) - pi;%az 116 | otherwise 117 | end 118 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 119 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 120 | phi_m(k, p) = pi - phi(k, p); 121 | theta_m(k, p) = pi - theta(k, p); 122 | else 123 | block_store(k, (l1-1)*L+l2) = 1; 124 | beta(k, p) = 0; 125 | continue; 126 | end 127 | else 128 | %take the reflector inside the cell 129 | pos_temp = zeros(1, 2); 130 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 131 | pos_temp(1, 1) = rand(1, 1) * Rmax; 132 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 133 | end 134 | switch l2 135 | case 1 136 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 137 | case 2 138 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 139 | case 3 140 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 141 | otherwise 142 | end 143 | d_temp = norm(pos_temp); 144 | pos_temp(1, 1) = d_temp * cos(angle_temp); 145 | pos_temp(1, 2) = d_temp * sin(angle_temp); 146 | pos_temp = pos_temp + base(l2, :)-base(l1, :); 147 | pos(k, 3) = norm(pos_temp); 148 | pos(k, 3) = norm([pos(k, 3), height]);%distance 149 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 150 | switch l1 151 | case 1 152 | phi(k, p) = phi(k, p) - pi / 3;%az 153 | case 2 154 | phi(k, p) = phi(k, p) + pi / 3;%az 155 | case 3 156 | phi(k, p) = phi(k, p) - pi;%az 157 | otherwise 158 | end 159 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 160 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 161 | phi_m(k, p) = pi - phi(k, p); 162 | theta_m(k, p) = pi - theta(k, p); 163 | end 164 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 165 | Aaz = -min(12 * phi(k, p)^2 / (70/180*pi)^2, 25); 166 | Ael = -min(12 * theta(k, p)^2 / (7/180*pi)^2, 20); 167 | D0 = -min(-Aaz-Ael, 25); 168 | D0 = 10^(D0*0.1); 169 | if p < 2 170 | if block_store(k, (l1-1)*L+l2) > 0 171 | else 172 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi); 173 | end 174 | else 175 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi) * 10^((-rand(1,1) * 5 - 15)*0.05);%-15~-20dB loss 176 | end 177 | hb = zeros(n_arr, 1); 178 | for nx = 0 : naz-1 179 | for ny = 0 : nel-1 180 | n = ny * naz+ 1 + nx; 181 | hb(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(naz-1)) * cos(theta(k, p)) * sin(phi(k, p)) + (ny-0.5*(nel-1)) * sin(theta(k, p)))); 182 | end 183 | end 184 | hm = zeros(m_arr, 1); 185 | for nx = 0 : maz-1 186 | for ny = 0 : mel-1 187 | n = ny * maz+ 1 + nx; 188 | hm(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(maz-1)) * cos(theta_m(k, p)) * sin(phi_m(k, p)) + (ny-0.5*(mel-1)) * sin(theta_m(k, p)))); 189 | end 190 | end 191 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) = ... 192 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) + beta(k, p) * hm * hb'; 193 | thetabb_store(k, (l1-1)*L*P+(l2-1)*P+p) = theta(k, p); 194 | phibb_store(k, (l1-1)*L*P+(l2-1)*P+p) = phi(k, p); 195 | betab_store(k, (l1-1)*L*P+(l2-1)*P+p) = abs(beta(k, p)); 196 | if l1==l2 197 | thetab_store(k, (l1-1)*P+p) = theta(k, p); 198 | phib_store(k, (l1-1)*P+p) = phi(k, p); 199 | thetam_store(k, (l1-1)*P+p) = theta_m(k, p); 200 | phim_store(k, (l1-1)*P+p) = phi_m(k, p); 201 | beta_store(k, (l1-1)*P+p) = abs(beta(k, p)); 202 | else 203 | end 204 | end 205 | end 206 | end 207 | end 208 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 209 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 210 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 211 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 212 | greedy_appr;%1 213 | maxmi_appr;%2 214 | pf_appr;%3 215 | proposed;%4-6 216 | disp([variable_n, ii]) 217 | end 218 | end 219 | capacity = capacity / Nite; 220 | jain = jain / Nite; 221 | %%%%%%%%%%%%%%%%%%%%%%%%%%%% 222 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 223 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 224 | 225 | h1 = subplot(1,2,1); 226 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 227 | plot(variable_s, capacity(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 228 | hold on 229 | plot(variable_s, capacity(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 230 | plot(variable_s, capacity(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 231 | plot(variable_s, capacity(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 232 | xlim([min(variable_s), max(variable_s)]) 233 | le = legend('Greedy','Max-min','PF','Proposed', 'Location', 'northwest'); 234 | set(le,'Fontname','Times') 235 | set(gca,'XTick',variable_s) 236 | xlabel('LOS blockage probability','Fontname','Times') 237 | ylabel('Sum rate (bps/Hz)','Fontname','Times') 238 | grid on%%%%%%%%%%%%%%%%%%%%%%%% 239 | h2 = subplot(1,2,2); 240 | plot(variable_s, jain(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 241 | hold on 242 | plot(variable_s, jain(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 243 | plot(variable_s, jain(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 244 | plot(variable_s, jain(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 245 | xlim([min(variable_s), max(variable_s)]) 246 | set(le,'Fontname','Times') 247 | set(gca,'XTick',variable_s) 248 | xlabel('LOS blockage probability','Fontname','Times') 249 | ylabel('Jain''s fairness index','Fontname','Times') 250 | grid on -------------------------------------------------------------------------------- /capacity_R.m: -------------------------------------------------------------------------------- 1 | clear; 2 | close all; 3 | L = 3; 4 | naz = 12; 5 | nel = 100; 6 | n_arr = naz * nel; 7 | maz = 2; 8 | mel = 2; 9 | m_arr = maz * mel; 10 | Rmin = 90; 11 | Rmax = 100; 12 | base = [0, 0; 0, 2 * Rmax; sqrt(3) * Rmax, Rmax;]; 13 | Nr = 4; 14 | P = 4; 15 | K = 20; 16 | variable_s = [10; 30; 50; 70; 90;]; 17 | Pvsigma2 = 1e18; 18 | height = 10; 19 | time_fre_resources = 20; 20 | f = 80*10^9;%1G bandwidth 21 | lambda = 3 * 10^8 / f; 22 | miu = 0.5; 23 | beta_m = 10.3 * pi / 180; 24 | Nite = 1e4; 25 | capacity = zeros(length(variable_s), 6); 26 | jain = zeros(length(variable_s), 6); 27 | angle = zeros(1, 2); 28 | U = zeros(n_arr, n_arr); 29 | for nx = 0 : naz-1 30 | for ny = 0 : nel-1 31 | angle(1, 2) = (-1+2*ny/nel);%el 32 | angle(1, 1) = (-1+2*nx/naz);%az 33 | n = ny * naz + nx + 1; 34 | for mx = 0 : naz-1 35 | for my = 0 : nel-1 36 | m = my * naz + 1 + mx; 37 | U(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(naz-1)) * angle(1, 1) + (my-0.5*(nel-1)) * angle(1, 2))) / sqrt(n_arr); 38 | end 39 | end 40 | end 41 | end 42 | Um = zeros(m_arr, m_arr); 43 | for nx = 0 : maz-1 44 | for ny = 0 : mel-1 45 | angle(1, 2) = (-1+2*ny/mel);%el 46 | angle(1, 1) = (-1+2*nx/maz);%az 47 | n = ny * maz + nx + 1; 48 | for mx = 0 : maz-1 49 | for my = 0 : mel-1 50 | m = my * maz + 1 + mx; 51 | Um(m, n) = exp(-1i * 2 * pi * miu * ((mx-0.5*(maz-1)) * angle(1, 1) + (my-0.5*(mel-1)) * angle(1, 2))) / sqrt(m_arr); 52 | end 53 | end 54 | end 55 | end 56 | for variable_n = 1 : length(variable_s) 57 | Rmin = variable_s(variable_n, 1); 58 | for ii = 1 : Nite 59 | H = zeros(m_arr, K*L*L*n_arr); 60 | p_store = zeros(K, L); 61 | beta_store = zeros(K, P*L); 62 | betab_store = zeros(K, P*L*L); 63 | thetab_store = zeros(K, P*L); 64 | thetabb_store = zeros(K, P*L*L); 65 | phib_store = zeros(K, P*L); 66 | phibb_store = zeros(K, P*L*L); 67 | thetam_store = zeros(K, P*L); 68 | phim_store = zeros(K, P*L); 69 | pos_store = zeros(K*L, 2); 70 | for l = 1 : L 71 | for k = 1 : K 72 | pos_temp = zeros(1, 2); 73 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 74 | pos_temp(1, 1) = rand(1, 1) * Rmax; 75 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 76 | end 77 | switch l 78 | case 1 79 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 80 | case 2 81 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 82 | case 3 83 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 84 | otherwise 85 | end 86 | d_temp = norm(pos_temp); 87 | pos_temp(1, 1) = d_temp * cos(angle_temp); 88 | pos_temp(1, 2) = d_temp * sin(angle_temp); 89 | pos_store((l-1)*K+k, :) = pos_temp;%relative to the serving BS 90 | end 91 | end 92 | pos = zeros(K, 3); 93 | theta = zeros(K, P); 94 | phi = zeros(K, P); 95 | beta = zeros(K, P); 96 | theta_m = zeros(K, P); 97 | phi_m = zeros(K, P); 98 | block_store = zeros(K, L*L); 99 | for l1 = 1 : L 100 | for l2 = 1 : L 101 | for k = 1 : K 102 | for p = 1 : P 103 | if 1==p 104 | pos_temp = pos_store((l2-1)*K+k, :) + base(l2, :)-base(l1, :);%%relative position of MS in the l2-th cell to l1-th BS 105 | pos(k, 3) = norm(pos_temp); 106 | pos(k, 3) = norm([pos(k, 3), height]);%distance 107 | if rand(1,1)>0.1 108 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 109 | switch l1 110 | case 1 111 | phi(k, p) = phi(k, p) - pi / 3;%az 112 | case 2 113 | phi(k, p) = phi(k, p) + pi / 3;%az 114 | case 3 115 | phi(k, p) = phi(k, p) - pi;%az 116 | otherwise 117 | end 118 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 119 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 120 | phi_m(k, p) = pi - phi(k, p); 121 | theta_m(k, p) = pi - theta(k, p); 122 | else 123 | block_store(k, (l1-1)*L+l2) = 1; 124 | beta(k, p) = 0; 125 | continue; 126 | end 127 | else 128 | %take the reflector inside the cell 129 | pos_temp = zeros(1, 2); 130 | while norm(pos_temp) < Rmin || norm(pos_temp) > Rmax || abs(atan(pos_temp(1, 2) / pos_temp(1, 1))) > pi / 3 131 | pos_temp(1, 1) = rand(1, 1) * Rmax; 132 | pos_temp(1, 2) = (rand(1, 1) * 2 - 1) * Rmax; 133 | end 134 | switch l2 135 | case 1 136 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi / 3; 137 | case 2 138 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) - pi / 3; 139 | case 3 140 | angle_temp = atan(pos_temp(1, 2) / pos_temp(1, 1)) + pi; 141 | otherwise 142 | end 143 | d_temp = norm(pos_temp); 144 | pos_temp(1, 1) = d_temp * cos(angle_temp); 145 | pos_temp(1, 2) = d_temp * sin(angle_temp); 146 | pos_temp = pos_temp + base(l2, :)-base(l1, :); 147 | pos(k, 3) = norm(pos_temp); 148 | pos(k, 3) = norm([pos(k, 3), height]);%distance 149 | phi(k, p) = asin(pos_temp(1, 2) / sqrt(pos_temp(1, 2)^2 + (pos_temp(1, 1) * cos(beta_m) + height * sin(beta_m))^2));%az 150 | switch l1 151 | case 1 152 | phi(k, p) = phi(k, p) - pi / 3;%az 153 | case 2 154 | phi(k, p) = phi(k, p) + pi / 3;%az 155 | case 3 156 | phi(k, p) = phi(k, p) - pi;%az 157 | otherwise 158 | end 159 | theta(k, p) = asin((pos_temp(1, 1) * sin(beta_m) - height * cos(beta_m)) / pos(k, 3));%el 160 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 161 | phi_m(k, p) = pi - phi(k, p); 162 | theta_m(k, p) = pi - theta(k, p); 163 | end 164 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 165 | Aaz = -min(12 * phi(k, p)^2 / (70/180*pi)^2, 25); 166 | Ael = -min(12 * theta(k, p)^2 / (7/180*pi)^2, 20); 167 | D0 = -min(-Aaz-Ael, 25); 168 | D0 = 10^(D0*0.1); 169 | if p < 2 170 | if block_store(k, (l1-1)*L+l2) > 0 171 | else 172 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi); 173 | end 174 | else 175 | beta(k, p) = sqrt(D0 * lambda^2 / (16 * pi^2 * pos(k, 3)^2)) * exp(1i * rand(1,1) * 2 * pi) * 10^((-rand(1,1) * 5 - 15)*0.05);%-15~-20dB loss 176 | end 177 | hb = zeros(n_arr, 1); 178 | for nx = 0 : naz-1 179 | for ny = 0 : nel-1 180 | n = ny * naz+ 1 + nx; 181 | hb(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(naz-1)) * cos(theta(k, p)) * sin(phi(k, p)) + (ny-0.5*(nel-1)) * sin(theta(k, p)))); 182 | end 183 | end 184 | hm = zeros(m_arr, 1); 185 | for nx = 0 : maz-1 186 | for ny = 0 : mel-1 187 | n = ny * maz+ 1 + nx; 188 | hm(n, 1) = exp(-1i * 2 * pi * miu * ((nx-0.5*(maz-1)) * cos(theta_m(k, p)) * sin(phi_m(k, p)) + (ny-0.5*(mel-1)) * sin(theta_m(k, p)))); 189 | end 190 | end 191 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) = ... 192 | H(:,(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l2-1)*K*n_arr+k*n_arr) + beta(k, p) * hm * hb'; 193 | thetabb_store(k, (l1-1)*L*P+(l2-1)*P+p) = theta(k, p); 194 | phibb_store(k, (l1-1)*L*P+(l2-1)*P+p) = phi(k, p); 195 | betab_store(k, (l1-1)*L*P+(l2-1)*P+p) = abs(beta(k, p)); 196 | if l1==l2 197 | thetab_store(k, (l1-1)*P+p) = theta(k, p); 198 | phib_store(k, (l1-1)*P+p) = phi(k, p); 199 | thetam_store(k, (l1-1)*P+p) = theta_m(k, p); 200 | phim_store(k, (l1-1)*P+p) = phi_m(k, p); 201 | beta_store(k, (l1-1)*P+p) = abs(beta(k, p)); 202 | else 203 | end 204 | end 205 | end 206 | end 207 | end 208 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 209 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 210 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 211 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 212 | greedy_appr;%1 213 | maxmi_appr;%2 214 | pf_appr;%3 215 | proposed;%4-6 216 | disp([variable_n, ii]) 217 | end 218 | end 219 | capacity = capacity / Nite; 220 | jain = jain / Nite; 221 | %%%%%%%%%%%%%%%%%%%%%%%%%%%% 222 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 223 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 224 | h1 = subplot(1,2,1); 225 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 226 | plot(variable_s, capacity(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 227 | hold on 228 | plot(variable_s, capacity(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 229 | plot(variable_s, capacity(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 230 | plot(variable_s, capacity(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 231 | xlim([min(variable_s), max(variable_s)]) 232 | le = legend('Greedy','Max-min','PF','Proposed', 'Location', 'northwest'); 233 | set(le,'Fontname','Times') 234 | set(gca,'XTick',variable_s) 235 | xlabel('Minimum MS to BS distance (m)','Fontname','Times') 236 | ylabel('Sum rate (bps/Hz)','Fontname','Times') 237 | grid on 238 | %%%%%%%%%%%%%%%%%%%%%%%% 239 | h2 = subplot(1,2,2); 240 | plot(variable_s, jain(1:length(variable_s), 1), 'k--s','LineWidth',1,'MarkerSize',10) 241 | hold on 242 | plot(variable_s, jain(1:length(variable_s), 2), 'k--*','LineWidth',1,'MarkerSize',10) 243 | plot(variable_s, jain(1:length(variable_s), 3), 'k--o','LineWidth',1,'MarkerSize',12) 244 | plot(variable_s, jain(1:length(variable_s), 4), 'k-^','LineWidth',1,'MarkerSize',10) 245 | xlim([min(variable_s), max(variable_s)]) 246 | set(le,'Fontname','Times') 247 | set(gca,'XTick',variable_s) 248 | xlabel('Minimum MS to BS distance (m)','Fontname','Times') 249 | ylabel('Jain''s fairness index','Fontname','Times') 250 | grid on -------------------------------------------------------------------------------- /capacity_SNR.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/anzhonghu/Beam-grouping-based-user-scheduling-in-multi-cell-millimeter-wave-MIMO-systems/34bbe45253f9bf885e2efcc9b84bff7c953c22af/capacity_SNR.m -------------------------------------------------------------------------------- /greedy_appr.m: -------------------------------------------------------------------------------- 1 | C_sel = zeros(K, L); 2 | K_ind = zeros(Nr, L); 3 | for l1 = 1 : L%j, user cell 4 | kc = 0; 5 | for n = 1 : Nr 6 | c_temp = zeros(K,1); 7 | if 1==n 8 | for k=1:K 9 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 10 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 11 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 12 | nn = ny * maz + nx + 1; 13 | wj = Um(:,nn); 14 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 15 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 16 | nn = ny * naz + nx + 1; 17 | Ul = U(:, nn); 18 | Zll = wj' * H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul; 19 | c_temp(k, 1) = abs(1 / (1/(Zll) * (1/(Zll))')); 20 | end 21 | else 22 | for k=1:K 23 | if C_sel(k,l1)>0 24 | else 25 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 26 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 27 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 28 | nn = ny * maz + nx + 1; 29 | wj_temp = [wj,Um(:,nn)]; 30 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 31 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 32 | nn = ny * naz + nx + 1; 33 | Ul_temp = [Ul,U(:, nn)]; 34 | Zll = zeros(kc+1,kc+1); 35 | for kkk = 1 : kc 36 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 37 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr) * Ul_temp; 38 | end 39 | kkk = kc + 1; 40 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 41 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul_temp; 42 | if cond(Zll)>1e3 43 | else 44 | c_temp(k, 1) = 1 / abs(trace(inv(Zll) * (inv(Zll))')); 45 | end 46 | end 47 | end 48 | end 49 | [c_temp_v,k] = max(c_temp); 50 | if c_temp_v > 0 51 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 52 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 53 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 54 | nn = ny * maz + nx + 1; 55 | if 1==n 56 | wj = Um(:,nn); 57 | else 58 | wj_temp = [wj,Um(:,nn)]; 59 | wj = wj_temp; 60 | end 61 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 62 | ny = floor((sin(thetab_store(k,(l1-1)*P+ps))+1)*nel*0.5); 63 | nn = ny * naz + nx + 1; 64 | if 1==n 65 | Ul = U(:, nn); 66 | else 67 | Ul_temp = [Ul,U(:, nn)]; 68 | Ul = Ul_temp; 69 | end 70 | C_sel(k,l1) = 1; 71 | kc = kc + 1; 72 | K_ind(kc, l1) = k; 73 | else 74 | break; 75 | end 76 | end 77 | switch l1 78 | case 1 79 | kc = sum(C_sel(:,l1)); 80 | Zjj_1 = zeros(kc,kc); 81 | for kkk = 1 : kc 82 | Zjj_1(kkk, :) = wj(:,kkk)' * ... 83 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr) * Ul; 84 | end 85 | case 2 86 | kc = sum(C_sel(:,l1)); 87 | Zjj_2 = zeros(kc,kc); 88 | for kkk = 1 : kc 89 | Zjj_2(kkk, :) = wj(:,kkk)' * ... 90 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 91 | end 92 | case 3 93 | kc = sum(C_sel(:,l1)); 94 | Zjj_3 = zeros(kc,kc); 95 | for kkk = 1 : kc 96 | Zjj_3(kkk, :) = wj(:,kkk)' * ... 97 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 98 | end 99 | otherwise 100 | end 101 | end 102 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 103 | meth_ind = 1; 104 | capa_cal; 105 | capacity(variable_n, meth_ind) = capacity(variable_n, meth_ind) + sum(sum(capacity_temp_in)) * time_fre_resources; 106 | jain_temp = 0; 107 | for l1 = 1 : L 108 | for k = 1 : K 109 | jain_temp = jain_temp + capacity_temp_in(k, l1)^2; 110 | end 111 | end 112 | jain_temp = (sum(sum(capacity_temp_in)))^2 / K / L / jain_temp; 113 | jain(variable_n, meth_ind) = jain(variable_n, meth_ind) + jain_temp; 114 | 115 | -------------------------------------------------------------------------------- /maxmi_appr.m: -------------------------------------------------------------------------------- 1 | capacity_cumu = zeros(K, L); 2 | meth_ind = 2; 3 | for tfr = 1 : time_fre_resources 4 | C_sel = zeros(K, L); 5 | K_ind = zeros(Nr, L); 6 | for l1 = 1 : L 7 | [~, Csel] = sort(capacity_cumu(:, l1), 'ascend'); 8 | kc = 0; 9 | for n = 1 : K 10 | if 1==n 11 | k = Csel(n,1); 12 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 13 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 14 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 15 | nn = ny * maz + nx + 1; 16 | wj = Um(:,nn); 17 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 18 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 19 | nn = ny * naz + nx + 1; 20 | Ul = U(:, nn); 21 | kc = kc + 1; 22 | C_sel(k,l1) = 1; 23 | K_ind(kc, l1) = k; 24 | else 25 | k = Csel(n,1); 26 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 27 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 28 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 29 | nn = ny * maz + nx + 1; 30 | wj_temp = [wj,Um(:,nn)]; 31 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 32 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 33 | nn = ny * naz + nx + 1; 34 | Ul_temp = [Ul,U(:, nn)]; 35 | Zll = zeros(kc+1,kc+1); 36 | for kkk = 1 : kc 37 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 38 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul_temp; 39 | end 40 | kkk = kc + 1; 41 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 42 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul_temp; 43 | if cond(Zll * Zll')>1e3 44 | else 45 | wj = wj_temp; 46 | Ul = Ul_temp; 47 | kc = kc + 1; 48 | C_sel(k,l1) = 1; 49 | K_ind(kc, l1) = k; 50 | end 51 | end 52 | if kc == Nr 53 | break; 54 | else 55 | end 56 | end 57 | switch l1 58 | case 1 59 | kc = sum(C_sel(:,l1)); 60 | Zjj_1 = zeros(kc,kc); 61 | for kkk = 1 : kc 62 | Zjj_1(kkk, :) = wj(:,kkk)' * ... 63 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 64 | end 65 | case 2 66 | kc = sum(C_sel(:,l1)); 67 | Zjj_2 = zeros(kc,kc); 68 | for kkk = 1 : kc 69 | Zjj_2(kkk, :) = wj(:,kkk)' * ... 70 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 71 | end 72 | case 3 73 | kc = sum(C_sel(:,l1)); 74 | Zjj_3 = zeros(kc,kc); 75 | for kkk = 1 : kc 76 | Zjj_3(kkk, :) = wj(:,kkk)' * ... 77 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 78 | end 79 | otherwise 80 | end 81 | end 82 | capa_cal; 83 | capacity_cumu = capacity_cumu + capacity_temp_in; 84 | end 85 | capacity(variable_n, meth_ind) = capacity(variable_n, meth_ind) + sum(sum(capacity_cumu)); 86 | jain_temp = 0; 87 | for l1 = 1 : L 88 | for k = 1 : K 89 | jain_temp = jain_temp + capacity_cumu(k, l1)^2; 90 | end 91 | end 92 | jain_temp = (sum(sum(capacity_cumu)))^2 / K / L / jain_temp; 93 | jain(variable_n, meth_ind) = jain(variable_n, meth_ind) + jain_temp; 94 | 95 | 96 | 97 | -------------------------------------------------------------------------------- /pf_appr.m: -------------------------------------------------------------------------------- 1 | capa_current_s = zeros(K, L); 2 | for l1 = 1 : L 3 | for k = 1 : K 4 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 5 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 6 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 7 | nn = ny * maz + nx + 1; 8 | wj = Um(:,nn); 9 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 10 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 11 | nn = ny * naz + nx + 1; 12 | Ul = U(:, nn); 13 | hll = wj' * H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul; 14 | capa_current_s(k, l1) = log2(1 + abs(hll)^2 * Pvsigma2); 15 | end 16 | end 17 | capacity_cumu = zeros(K, L); 18 | meth_ind = 3; 19 | for tfr = 1 : time_fre_resources 20 | C_sel = zeros(K, L); 21 | K_ind = zeros(Nr, L); 22 | for l1 = 1 : L 23 | [~, Csel] = sort(capa_current_s(:,l1) ./ capacity_cumu(:, l1), 'descend'); 24 | kc = 0; 25 | for n = 1 : K 26 | if 1==n 27 | k = Csel(n,1); 28 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 29 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 30 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 31 | nn = ny * maz + nx + 1; 32 | wj = Um(:,nn); 33 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 34 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 35 | nn = ny * naz + nx + 1; 36 | Ul = U(:, nn); 37 | kc = kc + 1; 38 | C_sel(k,l1) = 1; 39 | K_ind(kc, l1) = k; 40 | else 41 | k = Csel(n,1); 42 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 43 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 44 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 45 | nn = ny * maz + nx + 1; 46 | wj_temp = [wj,Um(:,nn)]; 47 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 48 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 49 | nn = ny * naz + nx + 1; 50 | Ul_temp = [Ul,U(:, nn)]; 51 | Zll = zeros(kc+1,kc+1); 52 | for kkk = 1 : kc 53 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 54 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul_temp; 55 | end 56 | kkk = kc + 1; 57 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 58 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul_temp; 59 | if cond(Zll * Zll')>1e3 60 | else 61 | wj = wj_temp; 62 | Ul = Ul_temp; 63 | kc = kc + 1; 64 | C_sel(k,l1) = 1; 65 | K_ind(kc, l1) = k; 66 | end 67 | end 68 | if kc == Nr 69 | break; 70 | else 71 | end 72 | end 73 | switch l1 74 | case 1 75 | kc = sum(C_sel(:,l1)); 76 | Zjj_1 = zeros(kc,kc); 77 | for kkk = 1 : kc 78 | Zjj_1(kkk, :) = wj(:,kkk)' * ... 79 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 80 | end 81 | case 2 82 | kc = sum(C_sel(:,l1)); 83 | Zjj_2 = zeros(kc,kc); 84 | for kkk = 1 : kc 85 | Zjj_2(kkk, :) = wj(:,kkk)' * ... 86 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 87 | end 88 | case 3 89 | kc = sum(C_sel(:,l1)); 90 | Zjj_3 = zeros(kc,kc); 91 | for kkk = 1 : kc 92 | Zjj_3(kkk, :) = wj(:,kkk)' * ... 93 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 94 | end 95 | otherwise 96 | end 97 | end 98 | capa_cal; 99 | capacity_cumu = capacity_cumu + capacity_temp_in; 100 | end 101 | capacity(variable_n, meth_ind) = capacity(variable_n, meth_ind) + sum(sum(capacity_cumu)); 102 | jain_temp = 0; 103 | for l1 = 1 : L 104 | for k = 1 : K 105 | jain_temp = jain_temp + capacity_cumu(k, l1)^2; 106 | end 107 | end 108 | jain_temp = (sum(sum(capacity_cumu)))^2 / K / L / jain_temp; 109 | jain(variable_n, meth_ind) = jain(variable_n, meth_ind) + jain_temp; 110 | 111 | 112 | 113 | -------------------------------------------------------------------------------- /proposed.m: -------------------------------------------------------------------------------- 1 | meth_ind = 4; 2 | C_sel = zeros(K, L); 3 | K_ind = zeros(Nr, L); 4 | flagl1 = zeros(L, 1); 5 | for lll1 = 1 : L 6 | l1=lll1; 7 | flagl1(l1, 1) = 1; 8 | hs = zeros(K, 1); 9 | gs = zeros(K, 1); 10 | interfusern = 0; 11 | for k = 1 : K 12 | cal_kl11; 13 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 14 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 15 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 16 | nn = ny * maz + nx + 1; 17 | wj = Um(:,nn); 18 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 19 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 20 | nn = ny * naz + nx + 1; 21 | Ul = U(:, nn); 22 | if 1==flag_kl1 23 | interfusern = interfusern + 1; 24 | gs(k, 1) = abs(wj' * ... 25 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul)^2; 26 | else 27 | hs(k, 1) = abs(wj' * ... 28 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul)^2; 29 | end 30 | end 31 | [~, hs_ind] = sort(hs,'descend'); 32 | [~, gs_ind] = sort(gs,'descend'); 33 | hs_ind = [hs_ind(1:K-interfusern,1);gs_ind(1:interfusern,1)]; 34 | kc = 0; 35 | for n = 1 : K 36 | k = hs_ind(n, 1); 37 | if 0==kc 38 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 39 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 40 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 41 | nn = ny * maz + nx + 1; 42 | wj = Um(:,nn); 43 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 44 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 45 | nn = ny * naz + nx + 1; 46 | Ul = U(:, nn); 47 | kc = kc + 1; 48 | C_sel(k,l1) = 1; 49 | K_ind(kc, l1) = k; 50 | else 51 | [~,ps] = max(beta_store(k, (l1-1)*P+1:l1*P)); 52 | nx = floor((cos(thetam_store(k, (l1-1)*P+ps)) * sin(phim_store(k, (l1-1)*P+ps))+1)*maz*0.5); 53 | ny = floor((sin(thetam_store(k, (l1-1)*P+ps))+1)*mel*0.5); 54 | nn = ny * maz + nx + 1; 55 | wj_temp = [wj,Um(:,nn)]; 56 | nx = floor((cos(thetab_store(k, (l1-1)*P+ps)) * sin(phib_store(k, (l1-1)*P+ps))+1)*naz*0.5); 57 | ny = floor((sin(thetab_store(k, (l1-1)*P+ps))+1)*nel*0.5); 58 | nn = ny * naz + nx + 1; 59 | Ul_temp = [Ul,U(:, nn)]; 60 | Zll = zeros(kc+1,kc+1); 61 | for kkk = 1 : kc 62 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 63 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul_temp; 64 | end 65 | kkk = kc + 1; 66 | Zll(kkk, :) = wj_temp(:,kkk)' * ... 67 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(k-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+k*n_arr) * Ul_temp; 68 | if cond(Zll)>1e3 69 | else 70 | wj = wj_temp; 71 | Ul = Ul_temp; 72 | kc = kc + 1; 73 | C_sel(k,l1) = 1; 74 | K_ind(kc, l1) = k; 75 | end 76 | end 77 | if kc == Nr 78 | break; 79 | else 80 | end 81 | end 82 | switch l1 83 | case 1 84 | kc = sum(C_sel(:,l1)); 85 | Zjj_1 = zeros(kc,kc); 86 | for kkk = 1 : kc 87 | Zjj_1(kkk, :) = wj(:,kkk)' * ... 88 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 89 | end 90 | case 2 91 | kc = sum(C_sel(:,l1)); 92 | Zjj_2 = zeros(kc,kc); 93 | for kkk = 1 : kc 94 | Zjj_2(kkk, :) = wj(:,kkk)' * ... 95 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 96 | end 97 | case 3 98 | kc = sum(C_sel(:,l1)); 99 | Zjj_3 = zeros(kc,kc); 100 | for kkk = 1 : kc 101 | Zjj_3(kkk, :) = wj(:,kkk)' * ... 102 | H(:,(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+(K_ind(kkk, l1)-1)*n_arr+1:(l1-1)*K*L*n_arr+(l1-1)*K*n_arr+K_ind(kkk, l1)*n_arr)* Ul; 103 | end 104 | otherwise 105 | end 106 | end 107 | capa_cal; 108 | %%%%%%%%%%%%%%%%%%%%%%%% 109 | capacity(variable_n, meth_ind) = capacity(variable_n, meth_ind) + sum(sum(capacity_temp_in)) * time_fre_resources; 110 | jain_temp = 0; 111 | for l1 = 1 : L 112 | for k = 1 : K 113 | jain_temp = jain_temp + capacity_temp_in(k, l1)^2; 114 | end 115 | end 116 | jain_temp = (sum(sum(capacity_temp_in)))^2 / K / L / jain_temp; 117 | jain(variable_n, meth_ind) = jain(variable_n, meth_ind) + jain_temp; 118 | 119 | 120 | 121 | --------------------------------------------------------------------------------