基于混沌加密的OFDM系统实现
基于混沌加密的OFDM系统实现，包括混沌序列生成、加密算法设计以及完整的OFDM系统集成
1. 混沌系统与序列生成
1.1 多种混沌系统实现
classdef ChaosEncryption
% 混沌加密系统
methods (Static)
function sequence = logistic_map(x0, r, N)
% Logistic混沌映射
% x0: 初始值, r: 控制参数, N: 序列长度
sequence = zeros(1, N);
sequence(1) = x0;
for i = 2:N
sequence(i) = r * sequence(i-1) * (1 - sequence(i-1));
end
end
function sequence = tent_map(x0, mu, N)
% Tent混沌映射
sequence = zeros(1, N);
sequence(1) = x0;
for i = 2:N
if sequence(i-1) < 0.5
sequence(i) = mu * sequence(i-1);
else
sequence(i) = mu * (1 - sequence(i-1));
end
end
end
function sequence = chebyshev_map(x0, k, N)
% Chebyshev混沌映射
sequence = zeros(1, N);
sequence(1) = x0;
for i = 2:N
sequence(i) = cos(k * acos(sequence(i-1)));
end
end
function [x, y] = henon_map(x0, y0, a, b, N)
% Henon混沌映射
x = zeros(1, N);
y = zeros(1, N);
x(1) = x0;
y(1) = y0;
for i = 2:N
x(i) = 1 - a * x(i-1)^2 + y(i-1);
y(i) = b * x(i-1);
end
end
function sequence = generate_chaos_bits(chaos_sequence, threshold)
% 将混沌序列转换为二进制序列
if nargin < 2
threshold = 0.5;
end
sequence = chaos_sequence > threshold;
end
function encrypted_bits = chaos_encrypt_bits(data_bits, chaos_bits)
% 使用混沌序列对二进制数据进行加密 (异或操作)
encrypted_bits = xor(data_bits, chaos_bits(1:length(data_bits)));
end
function decrypted_bits = chaos_decrypt_bits(encrypted_bits, chaos_bits)
% 使用混沌序列对加密数据进行解密 (异或操作)
decrypted_bits = xor(encrypted_bits, chaos_bits(1:length(encrypted_bits)));
end
end
end
1.2 增强型混沌序列生成器
classdef EnhancedChaosSystem
% 增强型混沌序列生成系统
properties
chaos_type % 混沌类型
parameters % 参数集合
initial_conditions % 初始条件
end
methods
function obj = EnhancedChaosSystem(type, varargin)
% 构造函数
obj.chaos_type = type;
p = inputParser;
switch lower(type)
case 'logistic'
addParameter(p, 'r', 3.99, @(x) x>0);
addParameter(p, 'x0', 0.5, @(x) x>0 && x<1);
case 'tent'
addParameter(p, 'mu', 1.999, @(x) x>0);
addParameter(p, 'x0', 0.5, @(x) x>0 && x<1);
case 'chebyshev'
addParameter(p, 'k', 4, @(x) x>0);
addParameter(p, 'x0', 0.5, @(x) x>0 && x<1);
case 'henon'
addParameter(p, 'a', 1.4, @(x) x>0);
addParameter(p, 'b', 0.3, @(x) x>0);
addParameter(p, 'x0', 0.1, @(x) x>0);
addParameter(p, 'y0', 0.1, @(x) x>0);
end
parse(p, varargin{:});
obj.parameters = p.Results;
obj.initial_conditions = p.Results;
end
function sequence = generate_sequence(obj, N, varargin)
% 生成混沌序列
p = inputParser;
addParameter(p, 'remove_transient', 1000, @(x) x>=0);
parse(p, varargin{:});
remove_N = p.Results.remove_transient;
total_N = N + remove_N;
switch lower(obj.chaos_type)
case 'logistic'
seq = ChaosEncryption.logistic_map(...
obj.initial_conditions.x0, ...
obj.parameters.r, total_N);
case 'tent'
seq = ChaosEncryption.tent_map(...
obj.initial_conditions.x0, ...
obj.parameters.mu, total_N);
case 'chebyshev'
seq = ChaosEncryption.chebyshev_map(...
obj.initial_conditions.x0, ...
obj.parameters.k, total_N);
case 'henon'
[seq, ~] = ChaosEncryption.henon_map(...
obj.initial_conditions.x0, ...
obj.initial_conditions.y0, ...
obj.parameters.a, obj.parameters.b, total_N);
end
% 去除瞬态
sequence = seq(remove_N+1:end);
end
function [encrypted_data, chaos_seq] = encrypt_data(obj, data, method)
% 加密数据
if nargin < 3
method = 'bit_xor';
end
N = length(data);
chaos_seq = obj.generate_sequence(N);
switch method
case 'bit_xor'
% 二进制异或加密
if islogical(data)
chaos_bits = ChaosEncryption.generate_chaos_bits(chaos_seq);
encrypted_data = ChaosEncryption.chaos_encrypt_bits(data, chaos_bits);
else
error('Bit XOR method requires binary input data');
end
case 'phase_rotation'
% 相位旋转加密 (用于OFDM符号)
encrypted_data = data .* exp(1j * 2 * pi * chaos_seq);
case 'subcarrier_permutation'
% 子载波置换加密
[~, perm_idx] = sort(chaos_seq);
encrypted_data = data(perm_idx);
case 'amplitude_modulation'
% 幅度调制加密
scaling_factors = 0.5 + chaos_seq; % 缩放因子在0.5-1.5之间
encrypted_data = data .* scaling_factors;
otherwise
error('Unknown encryption method');
end
end
function decrypted_data = decrypt_data(obj, encrypted_data, chaos_seq, method)
% 解密数据
if nargin < 4
method = 'bit_xor';
end
switch method
case 'bit_xor'
chaos_bits = ChaosEncryption.generate_chaos_bits(chaos_seq);
decrypted_data = ChaosEncryption.chaos_decrypt_bits(encrypted_data, chaos_bits);
case 'phase_rotation'
decrypted_data = encrypted_data .* exp(-1j * 2 * pi * chaos_seq);
case 'subcarrier_permutation'
[~, perm_idx] = sort(chaos_seq);
[~, inv_perm_idx] = sort(perm_idx);
decrypted_data = encrypted_data(inv_perm_idx);
case 'amplitude_modulation'
scaling_factors = 0.5 + chaos_seq;
decrypted_data = encrypted_data ./ scaling_factors;
end
end
function analyze_chaos_properties(obj, N)
% 分析混沌序列特性
sequence = obj.generate_sequence(N);
fprintf('混沌序列特性分析 (%s映射):\n', obj.chaos_type);
fprintf(' 序列长度: %d\n', N);
fprintf(' 均值: %.6f\n', mean(sequence));
fprintf(' 方差: %.6f\n', var(sequence));
fprintf(' 自相关 (lag=1): %.6f\n', autocorr(sequence, 1));
% 绘制特性图
figure('Position', [100, 100, 1200, 800]);
subplot(2, 3, 1);
plot(sequence(1:min(1000, N)), 'b-', 'LineWidth', 1);
title('混沌序列时域波形');
xlabel('样本索引');
ylabel('幅度');
grid on;
subplot(2, 3, 2);
hist(sequence, 50);
title('混沌序列直方图');
xlabel('幅度');
ylabel('频数');
grid on;
subplot(2, 3, 3);
plot(sequence(1:end-1), sequence(2:end), 'b.');
title('混沌吸引子');
xlabel('x(n)');
ylabel('x(n+1)');
grid on;
axis equal;
subplot(2, 3, 4);
autocorr(sequence, 50);
title('自相关函数');
grid on;
subplot(2, 3, 5);
[pxx, f] = pwelch(sequence - mean(sequence), [], [], [], 1);
semilogy(f, pxx, 'b-', 'LineWidth', 1);
title('功率谱密度');
xlabel('归一化频率');
ylabel('PSD');
grid on;
% Lyapunov指数估计
subplot(2, 3, 6);
lambda = estimate_lyapunov_exponent(sequence);
bar(1, lambda);
title(sprintf('Lyapunov指数估计: %.4f', lambda));
ylabel('Lyapunov指数');
grid on;
sgtitle(sprintf('%s混沌序列特性分析', upper(obj.chaos_type)));
end
end
end
function lambda = estimate_lyapunov_exponent(sequence)
% 估计Lyapunov指数 (简化方法)
N = length(sequence);
divergence = zeros(1, N-1);
for i = 1:N-1
divergence(i) = abs(sequence(i+1) - sequence(i));
end
lambda = mean(log(divergusion(divergence > 0) + eps));
end
2. OFDM系统基础实现
2.1 OFDM收发器类
classdef OFDMSystem
% OFDM系统基类
properties
Nfft % FFT点数
Ncp % 循环前缀长度
Nsc % 子载波数量
modulation_order % 调制阶数
sampling_freq % 采样频率
symbol_duration % 符号持续时间
subcarrier_spacing % 子载波间隔
pilot_pattern % 导频模式
equalizer_type % 均衡器类型
end
methods
function obj = OFDMSystem(config)
% 构造函数
obj.Nfft = config.Nfft;
obj.Ncp = config.Ncp;
obj.Nsc = config.Nsc;
obj.modulation_order = config.modulation_order;
obj.sampling_freq = config.sampling_freq;
obj.symbol_duration = (obj.Nfft + obj.Ncp) / obj.sampling_freq;
obj.subcarrier_spacing = obj.sampling_freq / obj.Nfft;
end
function modulated_symbols = modulate(obj, data_bits)
% 调制数据比特
switch obj.modulation_order
case 1 % BPSK
modulated_symbols = 1 - 2 * data_bits;
case 2 % QPSK
reshaped_bits = reshape(data_bits, 2, []);
symbols = (1 - 2 * reshaped_bits(1,:)) + ...
1j * (1 - 2 * reshaped_bits(2,:));
modulated_symbols = symbols / sqrt(2);
case 4 % 16QAM
reshaped_bits = reshape(data_bits, 4, []);
real_part = 2*(1-2*reshaped_bits(1,:)) .* ...
(1+2*reshaped_bits(2,:));
imag_part = 2*(1-2*reshaped_bits(3,:)) .* ...
(1+2*reshaped_bits(4,:));
modulated_symbols = (real_part + 1j * imag_part) / sqrt(10);
otherwise
error('Unsupported modulation order');
end
end
function data_bits = demodulate(obj, received_symbols)
% 解调接收符号
switch obj.modulation_order
case 1 % BPSK
data_bits = real(received_symbols) < 0;
case 2 % QPSK
real_bits = real(received_symbols) < 0;
imag_bits = imag(received_symbols) < 0;
data_bits = [real_bits; imag_bits];
data_bits = data_bits(:)';
case 4 % 16QAM
% 简化解调 - 实际应用中应该使用最大似然检测
real_vals = real(received_symbols);
imag_vals = imag(received_symbols);
real_bits = zeros(2, length(real_vals));
imag_bits = zeros(2, length(imag_vals));
% 判决区域
real_bits(1,:) = real_vals < 0;
real_bits(2,:) = abs(real_vals) > 2/sqrt(10);
imag_bits(1,:) = imag_vals < 0;
imag_bits(2,:) = abs(imag_vals) > 2/sqrt(10);
data_bits = [real_bits; imag_bits];
data_bits = data_bits(:)';
otherwise
error('Unsupported modulation order');
end
end
function ofdm_symbol = ifft_modulate(obj, freq_symbols)
% IFFT调制
% 确保输入符号长度正确
if length(freq_symbols) ~= obj.Nsc
error('Number of subcarriers does not match');
end
% 创建完整的FFT向量 (包含直流和镜像载波)
full_spectrum = zeros(1, obj.Nfft);
% 放置数据子载波 (居中放置)
start_idx = floor((obj.Nfft - obj.Nsc) / 2) + 1;
end_idx = start_idx + obj.Nsc - 1;
full_spectrum(start_idx:end_idx) = freq_symbols;
% IFFT
time_signal = ifft(full_spectrum, obj.Nfft);
% 添加循环前缀
cp = time_signal(end-obj.Ncp+1:end);
ofdm_symbol = [cp, time_signal];
end
function freq_symbols = fft_demodulate(obj, time_signal)
% FFT解调
% 移除循环前缀
if length(time_signal) ~= obj.Nfft + obj.Ncp
error('Invalid OFDM symbol length');
end
symbol_without_cp = time_signal(obj.Ncp+1:end);
% FFT
full_spectrum = fft(symbol_without_cp, obj.Nfft);
% 提取数据子载波
start_idx = floor((obj.Nfft - obj.Nsc) / 2) + 1;
end_idx = start_idx + obj.Nsc - 1;
freq_symbols = full_spectrum(start_idx:end_idx);
end
function [tx_signal, tx_symbols] = transmit(obj, data_bits)
% 完整的OFDM发射流程
num_bits_per_symbol = obj.Nsc * log2(obj.modulation_order);
num_symbols = ceil(length(data_bits) / num_bits_per_symbol);
% 零填充
padded_bits = [data_bits, zeros(1, num_symbols * num_bits_per_symbol - length(data_bits))];
tx_signal = [];
tx_symbols = [];
for sym = 1:num_symbols
% 提取当前符号的比特
start_bit = (sym-1) * num_bits_per_symbol + 1;
end_bit = sym * num_bits_per_symbol;
symbol_bits = padded_bits(start_bit:end_bit);
% 调制
modulated_data = obj.modulate(symbol_bits);
tx_symbols = [tx_symbols, modulated_data];
% OFDM调制
ofdm_sym = obj.ifft_modulate(modulated_data);
tx_signal = [tx_signal, ofdm_sym];
end
end
function [received_bits, eq_symbols] = receive(obj, rx_signal, channel, noise_variance)
% 完整的OFDM接收流程
symbol_length = obj.Nfft + obj.Ncp;
num_symbols = floor(length(rx_signal) / symbol_length);
received_bits = [];
eq_symbols = [];
for sym = 1:num_symbols
% 提取当前OFDM符号
start_sample = (sym-1) * symbol_length + 1;
end_sample = sym * symbol_length;
ofdm_symbol = rx_signal(start_sample:end_sample);
% OFDM解调
freq_symbols = obj.fft_demodulate(ofdm_symbol);
% 信道均衡 (简化)
if nargin >= 3 && ~isempty(channel)
% 频域均衡
H = fft(channel, obj.Nfft);
start_idx = floor((obj.Nfft - obj.Nsc) / 2) + 1;
end_idx = start_idx + obj.Nsc - 1;
H_data = H(start_idx:end_idx);
% ZF均衡
eq_freq_symbols = freq_symbols ./ H_data;
else
eq_freq_symbols = freq_symbols;
end
eq_symbols = [eq_symbols, eq_freq_symbols];
% 解调
symbol_bits = obj.demodulate(eq_freq_symbols);
received_bits = [received_bits, symbol_bits];
end
end
end
end
3. 混沌加密OFDM系统
3.1 集成混沌加密的OFDM系统
classdef ChaosEncryptedOFDM < OFDMSystem
% 基于混沌加密的OFDM系统
properties
chaos_system % 混沌系统
encryption_method % 加密方法
encryption_key % 加密密钥
end
methods
function obj = ChaosEncryptedOFDM(config)
% 构造函数
obj = obj@OFDMSystem(config);
if isfield(config, 'chaos_system')
obj.chaos_system = config.chaos_system;
else
% 默认使用Logistic映射
obj.chaos_system = EnhancedChaosSystem('logistic', 'r', 3.99, 'x0', 0.5);
end
if isfield(config, 'encryption_method')
obj.encryption_method = config.encryption_method;
else
obj.encryption_method = 'phase_rotation';
end
% 生成加密密钥
obj.encryption_key = obj.generate_encryption_key();
end
function key = generate_encryption_key(obj)
% 生成加密密钥
% 基于混沌序列生成加密密钥
key.chaos_sequence = obj.chaos_system.generate_sequence(1000);
key.method = obj.encryption_method;
key.timestamp = now;
end
function [encrypted_symbols, chaos_seq] = encrypt_ofdm_symbols(obj, symbols)
% 加密OFDM符号
N = length(symbols);
chaos_seq = obj.chaos_system.generate_sequence(N);
encrypted_symbols = obj.chaos_system.encrypt_data(...
symbols, chaos_seq, obj.encryption_method);
end
function decrypted_symbols = decrypt_ofdm_symbols(obj, encrypted_symbols, chaos_seq)
% 解密OFDM符号
decrypted_symbols = obj.chaos_system.decrypt_data(...
encrypted_symbols, chaos_seq, obj.encryption_method);
end
function [tx_signal, encryption_info] = transmit_encrypted(obj, data_bits)
% 发射加密的OFDM信号
num_bits_per_symbol = obj.Nsc * log2(obj.modulation_order);
num_symbols = ceil(length(data_bits) / num_bits_per_symbol);
% 零填充
padded_bits = [data_bits, zeros(1, num_symbols * num_bits_per_symbol - length(data_bits))];
tx_signal = [];
all_chaos_sequences = [];
for sym = 1:num_symbols
% 提取当前符号的比特
start_bit = (sym-1) * num_bits_per_symbol + 1;
end_bit = sym * num_bits_per_symbol;
symbol_bits = padded_bits(start_bit:end_bit);
% 调制
modulated_data = obj.modulate(symbol_bits);
% 混沌加密
[encrypted_data, chaos_seq] = obj.encrypt_ofdm_symbols(modulated_data);
all_chaos_sequences = [all_chaos_sequences; chaos_seq];
% OFDM调制
ofdm_sym = obj.ifft_modulate(encrypted_data);
tx_signal = [tx_signal, ofdm_sym];
end
encryption_info.chaos_sequences = all_chaos_sequences;
encryption_info.method = obj.encryption_method;
end
function received_bits = receive_encrypted(obj, rx_signal, encryption_info, channel, noise_variance)
% 接收并解密OFDM信号
symbol_length = obj.Nfft + obj.Ncp;
num_symbols = floor(length(rx_signal) / symbol_length);
if num_symbols ~= size(encryption_info.chaos_sequences, 1)
error('Number of symbols does not match encryption info');
end
received_bits = [];
for sym = 1:num_symbols
% 提取当前OFDM符号
start_sample = (sym-1) * symbol_length + 1;
end_sample = sym * symbol_length;
ofdm_symbol = rx_signal(start_sample:end_sample);
% OFDM解调
freq_symbols = obj.fft_demodulate(ofdm_symbol);
% 信道均衡
if nargin >= 4 && ~isempty(channel)
H = fft(channel, obj.Nfft);
start_idx = floor((obj.Nfft - obj.Nsc) / 2) + 1;
end_idx = start_idx + obj.Nsc - 1;
H_data = H(start_idx:end_idx);
eq_freq_symbols = freq_symbols ./ H_data;
else
eq_freq_symbols = freq_symbols;
end
% 混沌解密
chaos_seq = encryption_info.chaos_sequences(sym, :);
decrypted_symbols = obj.decrypt_ofdm_symbols(eq_freq_symbols, chaos_seq);
% 解调
symbol_bits = obj.demodulate(decrypted_symbols);
received_bits = [received_bits, symbol_bits];
end
end
function analyze_security_performance(obj, data_length)
% 分析安全性能
fprintf('=== 混沌加密OFDM系统安全性能分析 ===\n\n');
% 生成测试数据
test_bits = randi([0 1], 1, data_length);
% 原始传输
[tx_signal_plain, ~] = obj.transmit(test_bits);
% 加密传输
[tx_signal_enc, enc_info] = obj.transmit_encrypted(test_bits);
% 分析安全性
analyze_encryption_security(tx_signal_plain, tx_signal_enc, test_bits, obj, enc_info);
end
end
end
function analyze_encryption_security(plain_signal, enc_signal, original_bits, ofdm_system, enc_info)
% 分析加密安全性
figure('Position', [100, 100, 1400, 1000]);
% 时域信号比较
subplot(3, 3, 1);
plot(real(plain_signal(1:1000)), 'b-', 'LineWidth', 1.5, 'DisplayName', '明文');
hold on;
plot(real(enc_signal(1:1000)), 'r-', 'LineWidth', 1.5, 'DisplayName', '密文');
title('时域信号比较');
xlabel('样本索引');
ylabel('幅度');
legend;
grid on;
% 频域比较
subplot(3, 3, 2);
N = min(length(plain_signal), 1024);
f_plain = abs(fft(plain_signal(1:N)));
f_enc = abs(fft(enc_signal(1:N)));
freq = (0:N-1) / N * ofdm_system.sampling_freq / 1e6;
plot(freq, 10*log10(f_plain), 'b-', 'DisplayName', '明文');
hold on;
plot(freq, 10*log10(f_enc), 'r-', 'DisplayName', '密文');
title('频域特性比较');
xlabel('频率 (MHz)');
ylabel('功率谱密度 (dB)');
legend;
grid on;
% 星座图比较
subplot(3, 3, 3);
% 提取第一个OFDM符号的频域数据
symbol_len = ofdm_system.Nfft + ofdm_system.Ncp;
plain_freq = ofdm_system.fft_demodulate(plain_signal(1:symbol_len));
enc_freq = ofdm_system.fft_demodulate(enc_signal(1:symbol_len));
plot(real(plain_freq), imag(plain_freq), 'bo', 'DisplayName', '明文');
hold on;
plot(real(enc_freq), imag(enc_freq), 'rx', 'DisplayName', '密文');
title('星座图比较');
xlabel('同相分量');
ylabel('正交分量');
legend;
grid on;
axis equal;
% 自相关分析
subplot(3, 3, 4);
[acf_plain, lags] = xcorr(plain_signal(1:1000), 100, 'coeff');
[acf_enc, ~] = xcorr(enc_signal(1:1000), 100, 'coeff');
plot(lags, abs(acf_plain), 'b-', 'DisplayName', '明文');
hold on;
plot(lags, abs(acf_enc), 'r-', 'DisplayName', '密文');
title('自相关函数');
xlabel('延迟');
ylabel('自相关');
legend;
grid on;
% 互相关分析
subplot(3, 3, 5);
[ccf, lags] = xcorr(plain_signal(1:1000), enc_signal(1:1000), 100, 'coeff');
plot(lags, abs(ccf), 'g-', 'LineWidth', 1.5);
title('明文-密文互相关');
xlabel('延迟');
ylabel('互相关');
grid on;
% 熵分析
subplot(3, 3, 6);
entropy_plain = calculate_signal_entropy(plain_signal);
entropy_enc = calculate_signal_entropy(enc_signal);
bar([1, 2], [entropy_plain, entropy_enc]);
set(gca, 'XTickLabel', {'明文', '密文'});
ylabel('信息熵');
title('信号信息熵比较');
grid on;
% 密钥敏感性分析
subplot(3, 3, 7);
% 使用稍微不同的密钥解密
wrong_key = enc_info;
wrong_key.chaos_sequences(1, :) = wrong_key.chaos_sequences(1, :) + 1e-10;
try
decrypted_wrong = ofdm_system.receive_encrypted(enc_signal, wrong_key);
ber_wrong = sum(decrypted_wrong(1:length(original_bits)) ~= original_bits) / length(original_bits);
catch
ber_wrong = 0.5; % 完全解密失败
end
% 正确解密
decrypted_correct = ofdm_system.receive_encrypted(enc_signal, enc_info);
ber_correct = sum(decrypted_correct(1:length(original_bits)) ~= original_bits) / length(original_bits);
bar([1, 2], [ber_correct, ber_wrong]);
set(gca, 'XTickLabel', {'正确密钥', '错误密钥'});
ylabel('误码率');
title('密钥敏感性分析');
grid on;
% 加密方法比较
subplot(3, 3, 8);
methods = {'phase_rotation', 'subcarrier_permutation', 'amplitude_modulation'};
ber_values = zeros(1, length(methods));
for i = 1:length(methods)
temp_system = ofdm_system;
temp_system.encryption_method = methods{i};
[enc_sig_temp, enc_info_temp] = temp_system.transmit_encrypted(original_bits);
dec_bits_temp = temp_system.receive_encrypted(enc_sig_temp, enc_info_temp);
ber_values(i) = sum(dec_bits_temp(1:length(original_bits)) ~= original_bits) / length(original_bits);
end
bar(ber_values);
set(gca, 'XTickLabel', {'相位', '置换', '幅度'});
ylabel('解密BER');
title('加密方法性能比较');
grid on;
% 安全性指标总结
subplot(3, 3, 9);
security_metrics = calculate_security_metrics(plain_signal, enc_signal);
bar(1:length(security_metrics), cell2mat(security_metrics(2:2:end)));
set(gca, 'XTickLabel', security_metrics(1:2:end));
ylabel('指标值');
title('安全性指标总结');
grid on;
rotateXLabels(gca, 45);
sgtitle('混沌加密OFDM系统安全性能分析');
end
function entropy = calculate_signal_entropy(signal)
% 计算信号的信息熵
[counts, ~] = hist(real(signal), 50);
prob = counts / sum(counts);
prob = prob(prob > 0); % 移除零概率
entropy = -sum(prob .* log2(prob));
end
function metrics = calculate_security_metrics(plain_signal, enc_signal)
% 计算安全性指标
% 相关性
correlation = max(abs(xcorr(plain_signal, enc_signal, 'coeff')));
% 密钥空间大小 (估计)
key_space = 1e6; % 简化估计
% 敏感性
diff_signal = plain_signal - enc_signal;
sensitivity = mean(abs(diff_signal).^2) / mean(abs(plain_signal).^2);
metrics = {
'相关性', correlation, ...
'密钥空间', key_space, ...
'敏感性', sensitivity, ...
'明文熵', calculate_signal_entropy(plain_signal), ...
'密文熵', calculate_signal_entropy(enc_signal)
};
end
4. 完整的主程序与性能评估
4.1 主程序实现
function main_chaos_encrypted_ofdm()
% 混沌加密OFDM系统主程序
fprintf('=== 基于混沌加密的OFDM系统仿真 ===\n\n');
% 系统参数配置
ofdm_config.Nfft = 64;
ofdm_config.Ncp = 16;
ofdm_config.Nsc = 52;
ofdm_config.modulation_order = 2; % QPSK
ofdm_config.sampling_freq = 20e6;
% 混沌系统配置
chaos_system = EnhancedChaosSystem('logistic', 'r', 3.99, 'x0', 0.5);
% 创建混沌加密OFDM系统
encrypted_ofdm = ChaosEncryptedOFDM(ofdm_config);
encrypted_ofdm.chaos_system = chaos_system;
encrypted_ofdm.encryption_method = 'phase_rotation';
fprintf('系统参数:\n');
fprintf(' FFT点数: %d\n', encrypted_ofdm.Nfft);
fprintf(' 子载波数: %d\n', encrypted_ofdm.Nsc);
fprintf(' 循环前缀: %d\n', encrypted_ofdm.Ncp);
fprintf(' 调制方式: %s\n', get_modulation_name(encrypted_ofdm.modulation_order));
fprintf(' 加密方法: %s\n', encrypted_ofdm.encryption_method);
fprintf(' 混沌系统: %s\n', encrypted_ofdm.chaos_system.chaos_type);
% 生成测试数据
data_length = 10000;
original_bits = randi([0 1], 1, data_length);
fprintf('\n测试数据: %d bits\n', data_length);
% 性能比较测试
compare_performance(encrypted_ofdm, original_bits);
% 安全性分析
fprintf('\n进行安全性分析...\n');
encrypted_ofdm.analyze_security_performance(1000);
% 鲁棒性测试
fprintf('\n进行鲁棒性测试...\n');
test_robustness(encrypted_ofdm, original_bits);
fprintf('\n=== 仿真完成 ===\n');
end
function compare_performance(ofdm_system, original_bits)
% 性能比较：加密 vs 未加密
fprintf('\n=== 性能比较分析 ===\n');
% 未加密传输
fprintf('未加密传输...\n');
[tx_signal_plain, tx_symbols_plain] = ofdm_system.transmit(original_bits);
% 加密传输
fprintf('加密传输...\n');
[tx_signal_enc, enc_info] = ofdm_system.transmit_encrypted(original_bits);
% AWGN信道测试
snr_values = 0:2:20;
ber_plain = zeros(size(snr_values));
ber_enc = zeros(size(snr_values));
for i = 1:length(snr_values)
snr = snr_values(i);
% 未加密系统
rx_signal_plain = awgn(tx_signal_plain, snr, 'measured');
received_bits_plain = ofdm_system.receive(rx_signal_plain);
ber_plain(i) = sum(received_bits_plain(1:length(original_bits)) ~= original_bits) / length(original_bits);
% 加密系统
rx_signal_enc = awgn(tx_signal_enc, snr, 'measured');
received_bits_enc = ofdm_system.receive_encrypted(rx_signal_enc, enc_info);
ber_enc(i) = sum(received_bits_enc(1:length(original_bits)) ~= original_bits) / length(original_bits);
end
% 绘制性能曲线
figure('Position', [100, 100, 1200, 800]);
subplot(2, 2, 1);
semilogy(snr_values, ber_plain, 'bo-', 'LineWidth', 2, 'MarkerSize', 8, 'DisplayName', '未加密');
hold on;
semilogy(snr_values, ber_enc, 'rs-', 'LineWidth', 2, 'MarkerSize', 8, 'DisplayName', '加密');
xlabel('SNR (dB)');
ylabel('误码率 (BER)');
title('加密 vs 未加密系统性能比较');
legend;
grid on;
% 计算性能损失
performance_loss = ber_enc - ber_plain;
subplot(2, 2, 2);
plot(snr_values, performance_loss, 'g^-', 'LineWidth', 2, 'MarkerSize', 8);
xlabel('SNR (dB)');
ylabel('BER性能损失');
title('加密引入的性能损失');
grid on;
% 复杂度分析
subplot(2, 2, 3);
complexity_metrics = analyze_complexity(ofdm_system, length(original_bits));
bar(cell2mat(complexity_metrics(2:2:end)));
set(gca, 'XTickLabel', complexity_metrics(1:2:end));
ylabel('相对复杂度');
title('系统复杂度分析');
grid on;
% 吞吐量分析
subplot(2, 2, 4);
throughput = calculate_throughput(ber_plain, ber_enc, snr_values, ofdm_system);
plot(snr_values, throughput.plain, 'bo-', 'DisplayName', '未加密');
hold on;
plot(snr_values, throughput.encrypted, 'rs-', 'DisplayName', '加密');
xlabel('SNR (dB)');
ylabel('有效吞吐量 (Mbps)');
title('系统吞吐量比较');
legend;
grid on;
sgtitle('混沌加密OFDM系统性能分析');
end
function test_robustness(ofdm_system, original_bits)
% 鲁棒性测试
fprintf('进行系统鲁棒性测试...\n');
% 测试不同信道条件
channel_types = {'AWGN', 'Rayleigh', 'Rician'};
robustness_results = cell(length(channel_types), 1);
figure('Position', [100, 100, 1200, 600]);
for i = 1:length(channel_types)
channel_type = channel_types{i};
fprintf('测试信道: %s\n', channel_type);
% 生成加密信号
[tx_signal, enc_info] = ofdm_system.transmit_encrypted(original_bits);
% 应用不同信道
rx_signal = apply_channel(tx_signal, channel_type, 10); % SNR = 10dB
% 解密接收
received_bits = ofdm_system.receive_encrypted(rx_signal, enc_info);
ber = sum(received_bits(1:length(original_bits)) ~= original_bits) / length(original_bits);
robustness_results{i} = struct('channel', channel_type, 'ber', ber);
% 绘制星座图
subplot(2, 3, i);
symbol_len = ofdm_system.Nfft + ofdm_system.Ncp;
rx_freq = ofdm_system.fft_demodulate(rx_signal(1:symbol_len));
plot(real(rx_freq), imag(rx_freq), 'b.');
title(sprintf('%s信道 - BER: %.4f', channel_type, ber));
xlabel('同相分量');
ylabel('正交分量');
grid on;
axis equal;
end
% 密钥错误敏感性测试
subplot(2, 3, 4);
test_key_sensitivity(ofdm_system, original_bits);
% 参数敏感性测试
subplot(2, 3, 5);
test_parameter_sensitivity(ofdm_system, original_bits);
% 综合鲁棒性评分
subplot(2, 3, 6);
overall_robustness = evaluate_overall_robustness(robustness_results);
bar(overall_robustness.scores);
set(gca, 'XTickLabel', overall_robustness.metrics);
ylabel('评分 (0-10)');
title('系统鲁棒性综合评分');
grid on;
rotateXLabels(gca, 45);
sgtitle('混沌加密OFDM系统鲁棒性测试');
end
function name = get_modulation_name(order)
% 获取调制方式名称
switch order
case 1
name = 'BPSK';
case 2
name = 'QPSK';
case 4
name = '16QAM';
otherwise
name = sprintf('%d-QAM', 2^order);
end
end
function rx_signal = apply_channel(tx_signal, channel_type, snr)
% 应用信道模型
switch channel_type
case 'AWGN'
rx_signal = awgn(tx_signal, snr, 'measured');
case 'Rayleigh'
% 瑞利衰落信道
channel = (randn(1, 6) + 1j * randn(1, 6)) / sqrt(2);
rx_signal = conv(tx_signal, channel, 'same');
rx_signal = awgn(rx_signal, snr, 'measured');
case 'Rician'
% 莱斯衰落信道
K = 3; % K因子
direct_path = sqrt(K/(K+1));
scattered = sqrt(1/(2*(K+1))) * (randn(1, 4) + 1j * randn(1, 4));
channel = [direct_path, scattered];
rx_signal = conv(tx_signal, channel, 'same');
rx_signal = awgn(rx_signal, snr, 'measured');
end
end
function complexity = analyze_complexity(ofdm_system, data_length)
% 分析系统复杂度
base_operations = data_length * log2(ofdm_system.Nfft); % FFT复杂度基准
% 加密操作复杂度估计
switch ofdm_system.encryption_method
case 'phase_rotation'
encryption_ops = data_length * 2; % 复数乘法
case 'subcarrier_permutation'
encryption_ops = data_length * log2(data_length); % 排序复杂度
case 'amplitude_modulation'
encryption_ops = data_length; % 实数乘法
otherwise
encryption_ops = data_length;
end
total_ops = base_operations + encryption_ops;
complexity = {
'FFT运算', base_operations, ...
'加密运算', encryption_ops, ...
'总运算量', total_ops, ...
'复杂度增加', encryption_ops / base_operations
};
end
function throughput = calculate_throughput(ber_plain, ber_enc, snr_values, ofdm_system)
% 计算系统吞吐量
bits_per_symbol = ofdm_system.Nsc * log2(ofdm_system.modulation_order);
symbols_per_second = ofdm_system.sampling_freq / (ofdm_system.Nfft + ofdm_system.Ncp);
throughput.plain = (1 - ber_plain) * bits_per_symbol * symbols_per_second / 1e6; % Mbps
throughput.encrypted = (1 - ber_enc) * bits_per_symbol * symbols_per_second / 1e6; % Mbps
end
function test_key_sensitivity(ofdm_system, original_bits)
% 测试密钥敏感性
key_errors = logspace(-15, -5, 10);
ber_sensitivity = zeros(size(key_errors));
[tx_signal, enc_info] = ofdm_system.transmit_encrypted(original_bits);
for i = 1:length(key_errors)
wrong_info = enc_info;
wrong_info.chaos_sequences = wrong_info.chaos_sequences + key_errors(i);
try
received_bits = ofdm_system.receive_encrypted(tx_signal, wrong_info);
ber_sensitivity(i) = sum(received_bits(1:length(original_bits)) ~= original_bits) / length(original_bits);
catch
ber_sensitivity(i) = 0.5;
end
end
semilogx(key_errors, ber_sensitivity, 'ro-', 'LineWidth', 2);
xlabel('密钥误差');
ylabel('误码率');
title('密钥敏感性测试');
grid on;
end
function test_parameter_sensitivity(ofdm_system, original_bits)
% 测试参数敏感性
param_errors = linspace(0, 0.1, 10);
ber_sensitivity = zeros(size(param_errors));
for i = 1:length(param_errors)
% 创建参数错误的系统
wrong_system = ofdm_system;
wrong_system.chaos_system.parameters.r = wrong_system.chaos_system.parameters.r + param_errors(i);
[tx_signal, enc_info] = wrong_system.transmit_encrypted(original_bits);
try
% 用正确系统解密
received_bits = ofdm_system.receive_encrypted(tx_signal, enc_info);
ber_sensitivity(i) = sum(received_bits(1:length(original_bits)) ~= original_bits) / length(original_bits);
catch
ber_sensitivity(i) = 0.5;
end
end
plot(param_errors, ber_sensitivity, 'bo-', 'LineWidth', 2);
xlabel('参数误差');
ylabel('误码率');
title('参数敏感性测试');
grid on;
end
function robustness = evaluate_overall_robustness(results)
% 评估整体鲁棒性
metrics = {'信道适应性', '密钥敏感性', '参数鲁棒性', '噪声免疫性'};
scores = [8.5, 9.2, 7.8, 8.0]; % 示例评分
robustness.metrics = metrics;
robustness.scores = scores;
robustness.average_score = mean(scores);
end
% 运行主程序
main_chaos_encrypted_ofdm();
参考代码 基于混沌加密的ofdm码 www.youwenfan.com/contentcnl/80081.html
总结
主要特点：
- 多种混沌系统：Logistic、Tent、Chebyshev、Henon映射
- 多种加密方法：相位旋转、子载波置换、幅度调制
- 完整的OFDM系统：包含调制解调、FFT/IFFT、循环前缀
- 安全性分析：相关性分析、熵分析、密钥敏感性
- 性能评估：BER分析、吞吐量计算、复杂度分析
技术优势：
- 高安全性：混沌系统的初值敏感性和随机性
- 物理层安全：在物理层实现加密，增强系统安全性
- 灵活性：支持多种混沌系统和加密方法
- 实用性：可与现有OFDM系统兼容
应用价值：
- 为无线通信系统提供物理层安全解决方案
- 适用于5G/6G、WiFi、LTE等OFDM系统
- 支持安全性与性能的权衡分析
- 为通信安全研究提供完整仿真平台
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