优化 Wi-Fi 网络

simulationTime = 1;

rngSeed = 1;
rng(rngSeed,"combRecursive") % For reproducibility
numSTAs = 16;
staPositions = [randi([0,40],numSTAs,2) 3*ones(numSTAs,1)]; % 16 random 2-D integer points from 0 to 40, z = 3

maxNumAPs = 7;
apXPosition = optimvar("apXPosition",maxNumAPs,LowerBound=0,UpperBound=40,Type="integer");
apYPosition = optimvar("apYPosition",maxNumAPs,LowerBound=0,UpperBound=40,Type="integer");
apPositions = [apXPosition apYPosition 3*ones(maxNumAPs,1)]; % z-coordinate is fixed at 3

apEnable = optimvar("apEnable",maxNumAPs,LowerBound=0,UpperBound=1,Type="integer");

problem = optimproblem(Objective=sum(apEnable));

[staThroughput,numSTAsPerAP] = fcn2optimexpr(@simulateWLANNetwork,...
    apEnable,apPositions,staPositions,simulationTime,rngSeed,...
    ReuseEvaluation=true,Analysis="off",OutputSize={[1 numSTAs],[maxNumAPs 1]});

problem.Constraints.LowerLimitofSTAThroughput = (staThroughput >= 20);

problem.Constraints.MustHaveOneAP = (sum(apEnable) >= 1);
problem.Constraints.NumSTAsPerAP = (numSTAsPerAP >= apEnable);

opts = optimoptions("surrogateopt", ...
    MaxFunctionEvaluations=500, ... % Maximum evaluations of the objective before stopping
    MinSurrogatePoints=40, ... % Minimum number of initial sample points
    UseParallel=true); % Parallel evaluations

x0 = struct(apEnable=ones(maxNumAPs,1),...
    apXPosition=[0;12;28;40;28;12;20],...
    apYPosition=[20;0;0;20;40;40;20]);

tic
[sol,fval] = solve(problem,x0,Solver="surrogateopt",Options=opts)

toc

sol.apEnable

xpos = sol.apXPosition(logical(sol.apEnable))

ypos = sol.apYPosition(logical(sol.apEnable))

plot(xpos,ypos,"o",staPositions(:,1),staPositions(:,2),"*")
legend("AP","STA",Location="best")

function [stationThroughput,numSTAsPerAP] = simulateWLANNetwork(enableAP,apPositions,staPositions,simulationTime,rngSeed)
%simulateWLANNetwork Simulate Wi-Fi network
%
%   [stationThroughput,numSTAsPerAP] = simulateWLANNetwork(enableAP,
%   apPositions,staPositions,simulationTime,rngSeed) simulates the Wi-Fi
%   network with the specified layout of APs and STAs.
%
%   stationThroughput is a vector representing the throughput values in
%   Mbps.
%
%   numSTAsPerAP is a vector representing the number of STAs served by each AP.
%
%   enableAP is specified as an M-by-1 array of logical values, where 0
%   indicates that the AP is disabled and 1 indicates that the AP is
%   enabled. This variable is an optimization variable in the example.
%
%   apPositions is specified as an M-by-3 array of integers, where M
%   indicates the maximum number of APs and 3 indicates the number of
%   dimensions (x-, y-, and z-coordinates). This variable is an optimization
%   variable in the example.
%
%   staPositions is specified as an N-by-3 array of integers, where N
%   indicates the number of STAs and 3 indicates the number of dimensions
%   (x-, y-, and z-coordinates). This variable is a fixed variable in the example.
%
%   simulationTime is the duration of the simulation in seconds.
%
%   rngSeed is the seed used for the random number generator.

numAPs = size(apPositions,1);
numSTAs = size(staPositions,1);
numSTAsPerAP = zeros(numAPs,1); % Number of STAs associated with each AP
stationThroughput = zeros(1,numSTAs);

% Return if no APs are enabled
if sum(enableAP) == 0
    return
end

% Simulation configuration
rng(rngSeed,"combRecursive");
mcsIndex = 9;
txPower = 10;

% For each AP, assign a 20 MHz channel in the 5 GHz band.
channels = [36 40 44 48 52 56 60 64 100 104 108 112 116 120 124 128 132 136 140 144 149 153 157 161 165 169 173 177];
numChannels = numel(channels);
if numAPs <= numChannels
    apOperatingChannels = [5*ones(numAPs,1) channels(1:numAPs)'];
else % When the number of APs exceeds the number of available channels, reuse channels.
    numLoops = floor(numAPs/numChannels);
    for idx=1:numLoops
        apOperatingChannels(1+numChannels*(idx-1):idx*numChannels,:) = [5*ones(numChannels,1) channels(1:numChannels)'];
    end
    numExtraAPs = mod(numAPs,numChannels);
    if numExtraAPs > 0
        apOperatingChannels(1+numChannels*numLoops:numExtraAPs+numChannels*numLoops,:) = [5*ones(numExtraAPs,1) channels(1:numExtraAPs)'];
    end
end

% Initialize the wireless network simulator.
networkSimulator = wirelessNetworkSimulator.init;

% Configure the APs.
for idx = 1:numAPs
    accessPointCfg = wlanDeviceConfig(Mode="AP",MCS=mcsIndex,...
        TransmitPower=txPower,BandAndChannel=apOperatingChannels(idx,:)); % AP device configuration
    accessPoint(idx) = wlanNode(Name="AP" + idx,Position=apPositions(idx,:),...
        DeviceConfig=accessPointCfg);
end

% Configure the STAs.
for staId = 1:numSTAs
    % Find the nearest enabled AP and associate with that AP
    enabledAPIndices = find(enableAP);
    apID = findNearestAP(apPositions,staPositions(staId,:),enabledAPIndices);

    % Create the STA.
    stationCfg = wlanDeviceConfig(Mode="STA",MCS=mcsIndex,...
        TransmitPower=txPower,BandAndChannel=apOperatingChannels(apID,:)); % STA device configuration
    station(staId) = wlanNode(Name="STA" + staId,Position=staPositions(staId,:),...
        DeviceConfig=stationCfg);

    % Associate the station with the selected AP.
    associateStations(accessPoint(apID),station(staId),FullBufferTraffic="DL");
    numSTAsPerAP(apID) = numSTAsPerAP(apID) + 1;
end

% Set of WLAN nodes
nodes = [accessPoint station];

% Add the channel model.
% hSLSTGaxMultiFrequencySystemChannel.m is a supporting file when you run this example.
channel = hSLSTGaxMultiFrequencySystemChannel(nodes);
addChannelModel(networkSimulator,channelFunction(channel))

% Add nodes to the simulator and run the simulation.
addNodes(networkSimulator,nodes);
run(networkSimulator,simulationTime);

% Get statistics.
stats = statistics(nodes);

% Calculate the MAC layer throughput (in Mbps) at the STAs. Use the
% 'ReceivedPayloadBytes' statistic, which counts the total number of MSDU
% (MAC service data unit) bytes sent to an STA and received at the MAC layer.
% bytes of payload
for idx = 1:numSTAs
    stationThroughput(idx) = (stats(idx+numAPs).MAC.ReceivedPayloadBytes*8)/(simulationTime*1e6);
end
end

function nearestAPIndex = findNearestAP(apPositions,stationPosition,enabledAPIndices)
% findNearestAP Returns the index of the nearest enabled AP for each
% specified STA position.
%
%   nearestAPIndex = findNearestAP(apPositions,stationPosition,
%   enabledAPIndices) takes a list of AP positions and finds the position
%   that is nearest to the specified station position.
%
%   nearestAPIndex is the index of the AP in the specified apPositions vector
%   that is nearest to the stationPosition.
%
%   apPositions is a matrix of size M-by-3 representing a list of AP
%   positions, where M is the number of points and 3 is the number of
%   dimensions (x-, y-, and z- coordinates).
%
%   stationPosition is a vector of size 1-by-3 representing a specific
%   station position, where 3 is the number of dimensions (x-, y-, and
%   z- coordinates).
%
%   enabledAPIndices specifies the indices of the APs in apPositions that are
%   enabled for use.

% Initialize the variables.
minDistance = Inf;
nearestAPIndex = -1;

% Find the nearest enabled AP.
for apID = enabledAPIndices'
    % Calculate the distance for each reference point.
    distance = norm(apPositions(apID, :) - stationPosition);
    if distance < minDistance
        minDistance = distance;
        nearestAPIndex = apID;
    end
end
end