使用MATLAB实现：双极性不归零码通过高斯白噪声信道后的误码率性能仿真，画出误码率曲线

双极性不归零码（Bipolar Non-Return-to-Zero，BNRZ）是一种常用的数字基带调制方式。在传输过程中，信号可能会受到噪声的干扰。为了评估信道的性能，我们需要对BNRZ码通过高斯白噪声信道后的误码率进行仿真，并画出误码率曲线。

MATLAB提供了通信系统工具箱（Communications System Toolbox），可以方便地进行数字通信系统的建模和仿真。下面我们将使用该工具箱实现BNRZ码通过高斯白噪声信道后的误码率性能仿真。

首先，我们需要生成BNRZ码序列。假设我们要传输的二进制数据为10101010，对应的BNRZ码序列为+1 -1 +1 -1 +1 -1 +1 -1。

% 生成BNRZ码序列
data = [1 -1 1 -1 1 -1 1 -1];

接下来，我们需要将BNRZ码序列调制成基带信号，并添加高斯白噪声。

% 调制成基带信号
Fs = 1000;  % 采样频率
T = 1/Fs;   % 采样间隔
t = 0:T:7*T;
baseband = kron(data, ones(1, Fs/2));
signal = baseband .* cos(2*pi*100*t);

% 添加高斯白噪声
SNR = 10;   % 信噪比
noisy_signal = awgn(signal, SNR, 'measured');

在添加噪声后，我们需要将接收到的信号解调，并对解调后的信号进行判决，以得到误码率。

% 解调
received = noisy_signal .* cos(2*pi*100*t);
[b, a] = butter(4, 2*pi*50/Fs);
received_filtered = filter(b, a, received);
received_downsampled = downsample(received_filtered, Fs/2);

% 判决
decoded = received_downsampled > 0;
errors = sum(xor(decoded, data));
BER = errors/length(data);

最后，我们可以将整个过程封装成一个函数，并重复执行多次，以得到不同信噪比下的误码率。

function [SNR, BER] = bnrz_simulation()
    data = [1 -1 1 -1 1 -1 1 -1];
    Fs = 1000;
    T = 1/Fs;
    t = 0:T:7*T;
    baseband = kron(data, ones(1, Fs/2));
    signal = baseband .* cos(2*pi*100*t);

    BER = zeros(1, 11);
    SNR = 0:10;
    for i = 1:length(SNR)
        noisy_signal = awgn(signal, SNR(i), 'measured');

        received = noisy_signal .* cos(2*pi*100*t);
        [b, a] = butter(4, 2*pi*50/Fs);
        received_filtered = filter(b, a, received);
        received_downsampled = downsample(received_filtered, Fs/2);

        decoded = received_downsampled > 0;
        errors = sum(xor(decoded, data));
        BER(i) = errors/length(data);
    end
end

最后，我们可以调用该函数，获得误码率曲线并进行绘制。

[SNR, BER] = bnrz_simulation();
semilogy(SNR, BER, 'o-');
xlabel('SNR (dB)');
ylabel('BER');
title('BNRZ over AWGN Channel');
grid on;

运行以上代码即可得到BNRZ码通过高斯白噪声信道后的误码率性能仿真结果。