用基于最小二乘法做OFDM的信道估计，matlab代码

以下是基于最小二乘法的OFDM信道估计的matlab代码：

% 设置参数
N = 64; % 载波数
CP = N/4; % 循环前缀长度
SNR = 20; % 信噪比
M = 16; % 调制阶数
numSymbols = 1000; % 发送符号数
pilotIdx = [12, 26, 40, 54]; % 导频符号位置

% 生成QPSK调制的随机数据
data = randi([0 M-1], N - length(pilotIdx), numSymbols);
modData = qammod(data, M, 'gray');

% 在数据中插入导频符号
pilot = ones(length(pilotIdx), numSymbols);
modDataWithPilot = zeros(N, numSymbols);
modDataWithPilot(pilotIdx, :) = pilot;
modDataWithPilot(setdiff(1:N, pilotIdx), :) = modData;

% IFFT变换
timeData = ifft(modDataWithPilot, N);

% 循环前缀
timeDataWithCP = [timeData(N-CP+1:N, :); timeData];

% 信道
h = randn(1, numSymbols+1) + 1i*randn(1, numSymbols+1);
h = h/norm(h);

% 加噪声
noise = randn(size(timeDataWithCP)) + 1i*randn(size(timeDataWithCP));
SNR_linear = 10^(SNR/10);
noise_power = norm(h)^2 * N / SNR_linear;
rxData = timeDataWithCP .* repmat(h.', N, 1) + sqrt(noise_power/2) * noise;

% OFDM解调
rxData = rxData(CP+1:end, :);
freqData = fft(rxData, N);

% 最小二乘法信道估计
H = zeros(N, numSymbols+1);
P = zeros(length(pilotIdx), length(pilotIdx), numSymbols+1);
for i = 1:numSymbols+1
if ismember(i, pilotIdx)
P(:, :, i) = eye(length(pilotIdx));
else
P(:, :, i) = zeros(length(pilotIdx));
end
X = repmat(freqData(:, i), 1, length(pilotIdx));
H(:, i) = (P(:, :, i) * X) / (X' * P(:, :, i) * X);
end

% 去除导频符号的频域数据
freqDataWithoutPilot = freqData(setdiff(1:N, pilotIdx), :);

% 估计的信道频率响应
H_est = H(setdiff(1:N, pilotIdx), :);

% 理论误差
error = freqDataWithoutPilot - H_est .* repmat(freqData(setdiff(1:N, pilotIdx), 1), 1, numSymbols+1);

% 误差平均
mean_error = mean(error, 2);

% 修正后的信道估计
H_corrected = H_est + repmat(mean_error, 1, numSymbols+1);

% 数据解调
demodData = qamdemod(freqDataWithoutPilot ./ H_corrected, M, 'gray');

% 计算误码率
numErrors = sum(sum(demodData ~= data));
errorRate = numErrors / (numSymbols * length(data));

% 输出误码率
fprintf('Error rate: %f\n', errorRate);