用于大规模 MIMO 检测的近似消息传递（AMP）（Matlab代码实现）

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本文介绍了大规模MIMO技术中使用近似消息传递(AMP)算法进行高效信号检测的方法，强调了其在复杂环境下的优点和在低功耗设备上的适用性，同时讨论了AMP技术存在的计算资源消耗和对非线性特性的敏感性。

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🔥 内容介绍

在通信系统中，大规模 MIMO 技术已经成为了一个热门话题。大规模 MIMO 技术能够利用多个天线来传输和接收信号，从而提高了信号的可靠性和传输速度。然而，由于信号传输的复杂性，大规模 MIMO 技术也面临着一些挑战。其中一个挑战就是如何在大规模 MIMO 系统中进行检测。为了解决这个问题，近似消息传递（AMP）技术被提出，并被广泛应用于大规模 MIMO 系统中。

AMP 技术是一种基于概率推断的算法，它能够在大规模 MIMO 系统中高效地进行检测。AMP 技术的核心思想是将复杂的检测问题转化为简单的推断问题。在 AMP 技术中，每个接收天线都会生成一个消息，这个消息包含了接收到的信号和噪声的统计信息。这些消息会被传递到下一个节点，然后根据这些消息进行推断和计算。最终，AMP 技术能够得出准确的检测结果。

AMP 技术在大规模 MIMO 系统中的应用已经被证明是非常有效的。它能够在高速移动的环境下实现高速数据传输，并且能够在复杂的干扰环境下实现可靠的信号检测。此外，AMP 技术还能够在低功耗的设备上实现高效的检测，这对于物联网应用非常重要。

虽然 AMP 技术在大规模 MIMO 系统中的应用非常成功，但是它也存在一些局限性。例如，AMP 技术需要大量的计算资源来进行推断和计算，这可能会导致系统的延迟增加。此外，AMP 技术对于信号的噪声和非线性特性比较敏感，这可能会影响检测的准确性。

总之，近似消息传递（AMP）技术是一种非常有效的大规模 MIMO 检测技术。它能够在复杂的环境下实现高效的信号检测，并且能够在低功耗的设备上实现高效的检测。虽然 AMP 技术存在一些局限性，但是它的优点远远超过了缺点。因此，AMP 技术有望成为未来大规模 MIMO 系统中最常用的检测技术之一。

📣 部分代码

function [MinCost, Hamming,Best] = BBO(ProblemFunction, DisplayFlag, ProbFlag, RandSeed)% Biogeography-based optimization (BBO) software for minimizing a general function% INPUTS: ProblemFunction is the handle of the function that returns %         the handles of the initialization, cost, and feasibility functions.%         DisplayFlag = true or false, whether or not to display and plot results.%         ProbFlag = true or false, whether or not to use probabilities to update emigration rates.%         RandSeed = random number seed% OUTPUTS: MinCost = array of best solution, one element for each generation%          Hamming = final Hamming distance between solutions% CAVEAT: The "ClearDups" function that is called below replaces duplicates with randomly-generated%         individuals, but it does not then recalculate the cost of the replaced individuals.  if ~exist('DisplayFlag', 'var')    DisplayFlag = true;endif ~exist('ProbFlag', 'var')    ProbFlag = false;endif ~exist('RandSeed', 'var')    RandSeed = round(sum(100*clock));end[OPTIONS, MinCost, AvgCost, InitFunction, CostFunction, FeasibleFunction, ...    MaxParValue, MinParValue, Population] = Init(DisplayFlag, ProblemFunction, RandSeed);Population = CostFunction(OPTIONS, Population);OPTIONS.pmodify = 1; % habitat modification probabilityOPTIONS.pmutate = 0.005; % initial mutation probabilityKeep = 2; % elitism parameter: how many of the best habitats to keep from one generation to the nextlambdaLower = 0.0; % lower bound for immigration probabilty per genelambdaUpper = 1; % upper bound for immigration probabilty per genedt = 1; % step size used for numerical integration of probabilitiesI = 1; % max immigration rate for each islandE = 1; % max emigration rate, for each islandP = OPTIONS.popsize; % max species count, for each island% Initialize the species count probability of each habitat% Later we might want to initialize probabilities based on costfor j = 1 : length(Population)    Prob(j) = 1 / length(Population); end% Begin the optimization loopfor GenIndex = 1 : OPTIONS.Maxgen    % Save the best habitats in a temporary array.    for j = 1 : Keep        chromKeep(j,:) = Population(j).chrom;        costKeep(j) = Population(j).cost;    end    % Map cost values to species counts.    [Population] = GetSpeciesCounts(Population, P);    % Compute immigration rate and emigration rate for each species count.    % lambda(i) is the immigration rate for habitat i.    % mu(i) is the emigration rate for habitat i.    [lambda, mu] = GetLambdaMu(Population, I, E, P);    if ProbFlag        % Compute the time derivative of Prob(i) for each habitat i.        for j = 1 : length(Population)            % Compute lambda for one less than the species count of habitat i.            lambdaMinus = I * (1 - (Population(j).SpeciesCount - 1) / P);            % Compute mu for one more than the species count of habitat i.            muPlus = E * (Population(j).SpeciesCount + 1) / P;            % Compute Prob for one less than and one more than the species count of habitat i.            % Note that species counts are arranged in an order opposite to that presented in            % MacArthur and Wilson's book - that is, the most fit            % habitat has index 1, which has the highest species count.            if j < length(Population)                ProbMinus = Prob(j+1);            else                ProbMinus = 0;            end            if j > 1                ProbPlus = Prob(j-1);            else                ProbPlus = 0;            end            ProbDot(j) = -(lambda(j) + mu(j)) * Prob(j) + lambdaMinus * ProbMinus + muPlus * ProbPlus;        end        % Compute the new probabilities for each species count.        Prob = Prob + ProbDot * dt;        Prob = max(Prob, 0);        Prob = Prob / sum(Prob);     end    % Now use lambda and mu to decide how much information to share between habitats.    lambdaMin = min(lambda);    lambdaMax = max(lambda);    for k = 1 : length(Population)        if rand > OPTIONS.pmodify            continue;        end        % Normalize the immigration rate.        lambdaScale = lambdaLower + (lambdaUpper - lambdaLower) * (lambda(k) - lambdaMin) / (lambdaMax - lambdaMin);        % Probabilistically input new information into habitat i        for j = 1 : OPTIONS.numVar            if rand < lambdaScale                % Pick a habitat from which to obtain a feature                RandomNum = rand * sum(mu);                Select = mu(1);                SelectIndex = 1;                while (RandomNum > Select) & (SelectIndex < OPTIONS.popsize)                    SelectIndex = SelectIndex + 1;                    Select = Select + mu(SelectIndex);                end                Island(k,j) = Population(SelectIndex).chrom(j);            else                Island(k,j) = Population(k).chrom(j);            end        end    end    if ProbFlag        % Mutation        Pmax = max(Prob);        MutationRate = OPTIONS.pmutate * (1 - Prob / Pmax);        % Mutate only the worst half of the solutions        Population = PopSort(Population);        for k = round(length(Population)/2) : length(Population)            for parnum = 1 : OPTIONS.numVar                if MutationRate(k) > rand                    Island(k,parnum) = floor(MinParValue + (MaxParValue - MinParValue + 1) * rand);                end            end        end    end    % Replace the habitats with their new versions.    for k = 1 : length(Population)        Population(k).chrom = Island(k,:);    end    % Make sure each individual is legal.    Population = FeasibleFunction(OPTIONS, Population);    % Calculate cost    Population = CostFunction(OPTIONS, Population);    % Sort from best to worst    Population = PopSort(Population);    % Replace the worst with the previous generation's elites.    n = length(Population);    for k = 1 : Keep        Population(n-k+1).chrom = chromKeep(k,:);        Population(n-k+1).cost = costKeep(k);    end    % Make sure the population does not have duplicates.     Population = ClearDups(Population, MaxParValue, MinParValue);    % Sort from best to worst    Population = PopSort(Population);    % Compute the average cost    [AverageCost, nLegal] = ComputeAveCost(Population);    % Display info to screen    MinCost = [MinCost Population(1).cost];    AvgCost = [AvgCost AverageCost];    if DisplayFlag        disp(['The best and mean of Generation # ', num2str(GenIndex), ' are ',...            num2str(MinCost(end)), ' and ', num2str(AvgCost(end))]);    endendBest=Conclude(DisplayFlag, OPTIONS, Population, nLegal, MinCost);% Obtain a measure of population diversity% for k = 1 : length(Population)%     Chrom = Population(k).chrom;%     for j = MinParValue : MaxParValue%         indices = find(Chrom == j);%         CountArr(k,j) = length(indices); % array containing gene counts of each habitat%     end% endHamming = 0;% for m = 1 : length(Population)%     for j = m+1 : length(Population)%         for k = MinParValue : MaxParValue%             Hamming = Hamming + abs(CountArr(m,k) - CountArr(j,k));%         end%     end% end  if DisplayFlag    disp(['Diversity measure = ', num2str(Hamming)]);endreturn;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%function [Population] = GetSpeciesCounts(Population, P)% Map cost values to species counts.% This loop assumes the population is already sorted from most fit to least fit.for i = 1 : length(Population)    if Population(i).cost < inf        Population(i).SpeciesCount = P - i;    else        Population(i).SpeciesCount = 0;    endendreturn;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%function [lambda, mu] = GetLambdaMu(Population, I, E, P)% Compute immigration rate and extinction rate for each species count.% lambda(i) is the immigration rate for individual i.% mu(i) is the extinction rate for individual i.for i = 1 : length(Population)    lambda(i) = I * (1 - Population(i).SpeciesCount / P);    mu(i) = E * Population(i).SpeciesCount / P;endreturn;