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⛄ 内容介绍
This paper studies the optimal unmanned aerial vehicle (UAV) placement problem for wireless networking. The UAV operates as a flying wireless relay to provide coverage extension for a base station (BS) and deliver capacity boost to a user shadowed by obstacles. While existing methods rely on statistical models for potential blockage of a direct propagation link, we propose an approach capable of leveraging local terrain information to offer performance guarantees. The proposed method allows to strike the best trade-off between minimizing propagation distances to ground terminals and discovering good propagation conditions. The algorithm only requires several propagation parameters, but it is capable to avoid deep propagation shadowing and is proven to find the globally optimal UAV position. Only a local exploration over the target area is required, and the maximum length of search trajectory is linear to the geographical scale. Hence, it lends itself to online search. Significant throughput gains are found when compared to other positioning approaches based on statistical propagation models.
⛄ 部分代码
% Massive simulation
close all
clear
addpath(genpath('lib')),
Nue = 10000; % <- reduce this number to shorter simulation time (coarser results)
DATA = load('citymap/urbanMapSingleUserK2.mat');
U = DATA.U; PosBS = DATA.PosBS;
DATA = load('citymap/losStatistics.mat');
losStat.Plos = DATA.Plos;
losStat.ElvAngles = DATA.ElvAngles;
clear DATA
load('citymap/topologyK2.mat');
U.K = 2;
if U.K == 2
U.Alpha = [-21.4, -30.3];
U.Beta =[-36.92, -38.42];
elseif U.K == 3
U.Alpha = [-22, -28, -36];
U.Beta =[-28, -24, -22];
else
error('K should be 2 or 3.');
end
U.A0 = -20.8; U.B0 = -38.5;
U.A1 = U.Alpha(1); U.B1 = U.Beta(1);
U.A2 = U.Alpha(2); U.B2 = U.Beta(2);
Noise_dBm = -80;
Power_BS_dBm = 33;
Power_UAV_dBm = 33;
U.Noise = 10^(Noise_dBm/10) / 1000; % Watt in linear scale
U.Pb = 10^(Power_BS_dBm/10) / 1000;
U.Pd = 10^(Power_UAV_dBm/10) / 1000;
U.Hbs = 45; % meter, BS height
U.Hmin = 45; % meter, minimum UAV operation height
U.Hdrone = 50; % meter, UAV search height
stepSizeMeter = 5; % UAV search step size
fun = @(x,y) max(-log2(1 + U.Pd * real(x)), -log2(1 + U.Pb * real(y)));
fun0 = @(x) -log2(1 + U.Pb * x);
% Ergodic capacity
SNRs_dB = -10:2:20; Ks_dB = [9, -Inf];
Rerg = capacity_ergodic(Ks_dB, SNRs_dB);
fun1 = @(x,y) max(- max(0, ppval(spline(SNRs_dB, Rerg(1, :)), 10 * log10(U.Pd * real(x)))), ...
- log2(1 + U.Pb * real(y))); % UAV-UE_LOS(K-factor = 9dB,
fun2 = @(x,y) max(- max(0, ppval(spline(SNRs_dB, Rerg(2, :)), 10 * log10(U.Pd * real(x)))), ...
- log2(1 + U.Pb * real(y))); % UAV-UE_NLOS, Rayleigh fading
%%
N_scheme = 6;
tic
Nue = min(size(Topology, 1), Nue);
Rates0 = zeros(Nue, N_scheme);
strongUserIds = zeros(Nue, 1);
failIds = zeros(Nue, 1);
parfor i = 1:Nue
PosUE = Topology{i}.PosUE;
Blds = Topology{i}.Blds;
BldTypes = Topology{i}.BldTypes;
BldLines = Topology{i}.BldLines;
BldHeight = Topology{i}.BldHeight;
Nbld = size(Blds, 1);
los = IsLosK(PosUE, [PosBS, U.Hbs], BldLines, BldHeight, U.Hdrone, BldTypes);
if los == 1
strongUserIds(i) = 1;
% continue % We are only interested in the case where the direct BS-user link is blocked
end
urbanMap = struct();
urbanMap.BldLines = BldLines;
urbanMap.BldHeight = BldHeight;
urbanMap.BldTypes = BldTypes;
% Direct BS-user link
k = round((1 - los) * (U.K - 1) + 1); % propagation segment index
d = norm([PosBS, U.Hbs] - [PosUE, 0], 2);
snr = 10 ^ ((U.Alpha(k) * log10(d) + U.Beta(k)) / 10) / U.Noise;
F0 = fun0(snr);
try
% [Fmin3, Xhat3] = finduavpos3d(PosUE, PosBS, U, fun, stepSizeMeter, urbanMap);
% Fmin3 = min(Fmin3, F0);
Fmin3 = 0;
[~, Xhat2] = finduavpos(PosUE, PosBS, U, fun, stepSizeMeter, urbanMap);
los = IsLosK(PosUE, [Xhat2, U.Hdrone], BldLines, BldHeight, U.Hdrone, BldTypes);
Fmin2 = getcostf2DK_ergodic([Xhat2, U.Hdrone], [PosUE, 0], [PosBS, U.Hbs], los, U, fun1, fun2);
% Fmin2 = min(Fmin2, F0);
[~, Xhat1] = finduavpos1d(PosUE, PosBS, U, fun, stepSizeMeter, urbanMap);
los = IsLosK(PosUE, [Xhat1, U.Hdrone], BldLines, BldHeight, U.Hdrone, BldTypes);
Fmin1 = getcostf2DK_ergodic([Xhat1, U.Hdrone], [PosUE, 0], [PosBS, U.Hbs], los, U, fun1, fun2);
% Fmin1 = min(Fmin1, F0);
% [Fmin_exhst, Xhat_exhst] = finduavpos2d_exhst(PosUE, PosBS, U, fun, stepSizeMeter, urbanMap);
Fmin_exhst = Fmin3;
[~, XhatStat] = finduavposStat(PosUE, PosBS, U, fun, stepSizeMeter, urbanMap, losStat);
los = IsLosK(PosUE, [XhatStat, U.Hdrone], BldLines, BldHeight, U.Hdrone, BldTypes);
FminStat = getcostf2DK_ergodic([XhatStat, U.Hdrone], [PosUE, 0], [PosBS, U.Hbs], los, U, fun1, fun2);
% FminStat = min(FminStat, F0);
catch
Fmin1 = 0;
Fmin2 = 0;
Fmin3 = 0;
Fmin_exhst = 0;
FminStat = 0;
failIds(i) = 1;
end
Rates0(i, :) = - [F0, FminStat, Fmin1, Fmin2, Fmin3, Fmin_exhst];
end
toc
%% Plot results
my_line_styles = {'-', '--', '-.', ':'}.';
Alg_scheme_name = {
'Direct BS-User linkxx'
'Probabilistic Alg'
'Simple Search'
'Proposed'
'Proposed (3D)'
'Exhaustive'
};
schemes_to_show = [1 2 3 4 6];
N_scheme_to_show = length(schemes_to_show);
validUserId = failIds < 1;
Rates = Rates0(validUserId, :);
Nue = size(Rates, 1);
maxdata = max(Rates(:));
Npt = 40;
XI = sort([0.1 0.17 0.3 0.5 (0:1/(Npt - 1 - 4):1) * maxdata], 'ascend');
X_data = zeros(Npt, N_scheme_to_show);
F_data = zeros(Npt, N_scheme_to_show);
for i = 1:N_scheme_to_show
n = schemes_to_show(i);
r_vec = Rates(:, n);
[F1,X1] = ksdensity(r_vec, XI, 'function', 'cdf');
X_data(:, i) = X1(:);
F_data(:, i) = F1;
end
figure(1),
h = plot(X_data, F_data,'linewidth', 2);
set(gca, 'FontSize', 14);
legend(Alg_scheme_name{schemes_to_show}, 'location', 'southeast');
xlim([0 ceil(max(Rates(:)))]);
set(gca, 'YTick', 0:0.2:1);
xlabel('bps/Hz');
ylabel('CDF');
tune_figure,
set(h(1), 'linewidth', 2);
set(h(1), 'Marker', '*', 'Markersize', 6);
set(h(1), 'LineStyle', ':');
set(h(2), 'LineStyle', '-.');
set(h(3), 'LineStyle', ':');
set(h(4), 'LineStyle', '-');
set(h(4), 'LineWidth', 3);
set(h(5), 'linestyle', '--');
set(h(5), 'LineWidth', 3);
% ----
schemes_to_show = [1 2 3 4];
figure(2),
rateNoUav = Rates(:, 1);
[~, sortedIndex] = sort(rateNoUav, 'ascend');
low20percentileIndex = sortedIndex(1:round(Nue * 0.2));
high20percentileIndex = sortedIndex(round(Nue * 0.8): end);
RateLow = mean(Rates(low20percentileIndex, schemes_to_show), 1);
RateMean = mean(Rates(:, schemes_to_show), 1);
RateHigh = mean(Rates(high20percentileIndex, schemes_to_show), 1);
h = bar([RateLow
RateMean
RateHigh]);
set(gca, 'FontSize', 14);
set(h, 'linewidth', 2);
ylim([0, 10]);
legend(Alg_scheme_name{schemes_to_show}, 'location', 'northwest');
set(gca, 'XTickLabel', {'20th percentile', 'Mean', 'Top 20th percentile'});
set(gca, 'YTick', 0:2:10);
ylabel('Average end-to-end throughput [bps/Hz]');
% label the bars
Xdata = [RateLow
RateMean
RateHigh];
bartext = [];
for i = 1:size(Xdata, 1)
for j = 1:size(Xdata, 2)
bartext(i, j) = text(i + (j - 2.5) * 0.18, Xdata(i, j) + 0.05, ...
sprintf('%1.2f', Xdata(i, j)), 'fontsize', 12);
end
end
% Use the handles TH to modify some properties
set(bartext,'Horizontalalignment','center',...
'verticalalignment','bottom') ;
tune_figure,
[im_hatch,colorlist] = applyhatch_pluscolor(gcf,'\-x./+',0,0,[],150,2,2);
⛄ 运行结果
编辑
编辑
编辑
⛄ 参考文献
[1] Chen J , Gesbert D . Efficient Local Map Search Algorithms for the Placement of Flying Relays[J]. 2018.
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