16QAM-调制解调MATLAB

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clc
clear
close all
% Title:  16QAM调制与解调 %

M = 16;                                 % 调制阶数
L_data = 10000;                       % 数据长度
L_symbol = L_data/log2(M);              % 符号长度
data = round(rand(1,L_data));           % 原始数据
EbN0_dB = 0:14;                         % Eb/N0 dB形式
EbN0 = 10.^(EbN0_dB/10);                % 每比特能量/噪声
EsN0 = log2(M) * EbN0;                  % 每符号能量/噪声
error = zeros(1,length(EbN0_dB));       % 预置错误符号个数
ser = zeros(1,length(EbN0_dB));         % 预置仿真误符号率

tser_16QAM = zeros(1,length(EbN0_dB));  % 预置16QAM理论误符号率
% 16QAM调制
send = zeros(1,L_symbol);               % 预设发送信号
send_set = [-3+3j,-1+3j,1+3j,3+3j,...
            -3+1j,-1+1j,1+1j,3+1j,...
            -3-1j,-1-1j,1-1j,3-1j,...
            -3-3j,-1-3j,1-3j,3-3j];     % 发射端星座点
Es_avg = sum(abs(send_set).^2) / length(send_set);
N0 = Es_avg ./ EsN0;
for q = 1:L_symbol
    if (data(4*q-3:4*q) == [1,0,1,1])
        send(q) = send_set(1);          % 1001 => -3+3j
    elseif (data(4*q-3:4*q) == [1,0,0,1])
        send(q) = send_set(2);          % 1001 => -1+3j
    elseif (data(4*q-3:4*q) == [1,1,1,0])
        send(q) = send_set(3);          % 1110 => +1+3j
    elseif (data(4*q-3:4*q) == [1,1,1,1])
        send(q) = send_set(4);          % 1111 => +3+3j
    elseif (data(4*q-3:4*q) == [1,0,1,0])
        send(q) = send_set(5);          % 1010 => -3+1j
    elseif (data(4*q-3:4*q) == [1,0,0,0])
        send(q) = send_set(6);          % 1000 => -1+1j
    elseif (data(4*q-3:4*q) == [1,1,0,0])
        send(q) = send_set(7);          % 1100 => +1+1j
    elseif (data(4*q-3:4*q) == [1,1,0,1])
        send(q) = send_set(8);          % 1101 => +3+1j
    elseif (data(4*q-3:4*q) == [0,0,0,1])
        send(q) = send_set(9);          % 0001 => -3-1j
    elseif (data(4*q-3:4*q) == [0,0,0,0])
        send(q) = send_set(10);         % 0000 => -1-1j
    elseif (data(4*q-3:4*q) == [0,1,0,0])
        send(q) = send_set(11);         % 0100 => +1-1j
    elseif (data(4*q-3:4*q) == [0,1,1,0])
        send(q) = send_set(12);         % 0110 => +3-1j
    elseif (data(4*q-3:4*q) == [0,0,1,1])
        send(q) = send_set(13);         % 0011 => -3-3j
    elseif (data(4*q-3:4*q) == [0,0,1,0])
        send(q) = send_set(14);         % 0010 => -1-3j
    elseif (data(4*q-3:4*q) == [0,1,0,1])
        send(q) = send_set(15);         % 0101 => +1-3j
    else
        send(q) = send_set(16);         % 0111 => +3-3j
    end
end
for q = 1:length(EbN0_dB)
    noise = sqrt(N0(q)/2)*randn(1,L_symbol) + 1j*sqrt(N0(q)/2)*randn(1,L_symbol);   % AWGN
    receive = (send + noise);       % 接收信号
    detect = zeros(1,L_symbol);         % 预置检测信号
    distance = zeros(1,M);              % 解调：距离检测 
    for t = 1:L_symbol
        for w = 1:M
            distance(w) = norm(receive(t) - send_set(w))^2;     % 接收信号到所有星座点的距离
        end
        pos = find(distance == min(distance));      % 最小距离星座点的位置
        detect(t) = send_set(pos);                  % 解调后的符号
        if (detect(t) ~= send(t)) 
            error(q) = error(q) + 1;                % 统计错误符号数
        end
    end
    ser(q) = error(q)/L_symbol;                     % 16QAM仿真误符号率
           
    tser_16QAM(q) = 3*qfunc(sqrt(4/5*EbN0(q)))*(1-3/4*qfunc(sqrt(4/5*EbN0(q))));   % 16QAM理论误符号率
end
figure
semilogy(EbN0_dB,ser,'o',EbN0_dB,tser_16QAM,'b');     % 画图
grid on;                                        % 坐标轴开启
                   
xlabel('Eb/N0 (dB)');                           % 横坐标
ylabel('SER');                                  % 纵坐标
legend('16QAM仿真误符号率','16QAM理论误符号率');   % 图例