目录

1：AWGNChannelNoise Level

2：Relationship Between EsN0 and EbN0

3：Relationship Between EsN0 and SNR

4：仿真

5：计算结果

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1：AWGNChannelNoise Level

Typical quantities used to describe the relative power of noise in anAWGNchannelinclude

• Signal-to-noise ratio (SNR) per sample. SNR is the actual input parameter to theawgnfunction.

• Ratio of bit energy to noise power spectral density (EbN0). This quantity is used byBER AnalyzerTool and performance evaluation functions in this toolbox.

• Ratio of symbol energy to noise power spectral density (EsN0)

简单的解释是：

SNR表示每隔一次采样点的信号噪声比

EbN0表示每隔比特能量与噪声功率谱密度的比值

EsN0表示每个符号能量与噪声功率谱密度之比

2：Relationship Between EsN0 and EbN0

The relationship between EsN0 and EbN0, both expressed in dB, is as follows:

Es/N0(dB)=Eb/N0(dB) 10log10(k)

where k is the number of information bits per symbol.

In a communications system,kmight be influenced by the size of the modulation alphabet or the code rate of an error-control code. For example, in a system using a rate-1/2 code and 8-PSK modulation, the number of information bits per symbol (k) is the product of the code rate and the number of coded bits per modulated symbol. Specifically, (1/2) log2(8) = 3/2. In such a system, three information bits correspond to six coded bits, which in turn correspond to two 8-PSK symbols.

简单的解释是：

EsN0与EbN0的关系式

Es/N0(dB)=Eb/N0(dB) 10log10(k)

假设与信道编码无关bpsk，则k为log2^2=1，假设为qpsk，则k为log2^4=4;

3：Relationship Between EsN0 and SNR

The relationship between EsN0 and SNR, both expressed in dB, is as follows:

Es/N0(dB)=10log10(Tsym/Tsamp) SNR(dB)forcomplexinputsignalsEs/N0(dB)=10log10(0.5Tsym/Tsamp) SNR(dB)forrealinputsignals

whereTsymis the symbol period of the signal andTsampis the sampling period of the signal.

For a complex baseband signal oversampled by a factor of 4, the EsN0 exceeds the corresponding SNR by 10 log10(4).

Derivation for Complex Input Signals.You can derive the relationship between EsN0 and SNR for complex input signals as follows:

Es/N0(dB)=10log10((S?Tsym)/(N/Bn))

=10log10((TsymFs)?(S/N))

=10log10(Tsym/Tsamp) SNR(dB)

where

• S= Input signal power, in watts

• N= Noise power, in watts

• Bn= Noise bandwidth, in Hertz =Fs= 1/Tsamp.

• Fs= Sampling frequency, in Hertz

可以获得上述标红公式EbN0和SNR关系

SNR = EbN0 10log10(nBits*coderate) - 10log10(0.5or1 * upfactor);

参数说明：

Coderate：编码码率

nBits：每个符号或码元中的信息比特数

例如：BPSK的nBits为1、QPSK的nBits为2、8PSK的nBits为3……

BPSK中把1，0映射为±1时为实数，最后一项为0.5*……

若将1、0映射为1 j和-1-j，最后一项是复数*……

4：仿真

EsN0与SNR关系验证

N = 300; % 符号个数 sym = randi([0 1],1,N); Fs = 9600; RB = 200; alpha = 0.3; % 滚降系数 fc = 3000; % 载波 fd = Fs/RB; % 过采倍数 EsN0 = 15; % 符号信噪比 dB为单位 LinEsN0 = 10^(EsN0/10); % 线性单位的EsN0 SNR = EsN0 - 10*log10(Fs/RB); % SNR 以dB为单位 %% 基带信号 M = 2; Len = N*Fs/RB; t = 0:1/Fs:(Len-1)/Fs; pha_bpsk = pskmod(sym,M); % 生成相位 figure;plot(pha_bpsk,'.b','MarkerSize',15); title('BPSK星座图；  h = rcosine(RB,Fs,'fir/sqrt',alpha); % 根升余弦成形 bas_bpsk = rcosflt(pha_bpsk,RB,Fs,'filter',h).'; delay=(length(h) 1)/2; %%%时延
bas_bpsk=bas_bpsk(delay:end-delay+1);
sig_bpsk_pure = bas_bpsk.*exp(1j*2*pi*fc*t);
sig_bpsk_n = awgn(sig_bpsk_pure,SNR,'measured');

% EsN0 SNR的关系
sigPower = sum(abs(sig_bpsk_pure(:)).^2)/numel(sig_bpsk_pure); % 信号功率
sigma_n2=sigPower/10^(SNR/10); % 噪声功率
noise = sqrt(sigma_n2/2)* (randn(size(sig_bpsk_pure)) + 1i*randn(size(sig_bpsk_pure))); % 生成复高斯噪声
nlen = length(noise);
Et = sum(abs(noise).^2); % 噪声能量（时域）
Ef = sum(abs(fft(noise)/sqrt(nlen)).^2);% 噪声能量（频域）
wd = ones(1,fd); % 积分窗，长度为一个符号采样点数
Es = mean(conv(abs(sig_bpsk_pure).^2,wd)); % 单个符号的能量（时域符号周期积分求平均的方法）
Es1 = sum(abs(sig_bpsk_pure(:)).^2)/N; % 单个符号的能量（总能量除以符号个数）
N0 = mean(abs(noise).^2); % 噪声双边功率谱密度 通过时域求得
N0pri = mean(abs(fft(noise)/sqrt(nlen)).^2); % 噪声双边功率谱密度 通过频域求得
EsN0pri = Es/N0; % 通过计算符号能量和噪声双边功率谱密度得到的EsN0
SNRpri = 10*log10(sigPower/sigma_n2); % 信噪比

5：计算结果

代码中EsN0设置为15dB，计算结果因生成的随机符号序列不同可能会稍有不同，但都满足以上分析，计算结果分享如下

噪声能量
Et = 450.0291
Ef = 450.0291

信号功率
sigPower = 0.0208

噪声功率
sigma_n2 = 0.0315

信号单个符号能量
Es = 0.9928
Es1 = 0.9960

噪声双边功率谱密度
N0 = 0.0313
N0pri = 0.0313

EsN0线性单位值
LinEsN0 = 31.6228

EsN0通过Es/N0得到的值
EsN0pri = 31.7677

由公式得到的SNR值（dB为单位）
SNR = -1.8124

由10*log10(信号功率/噪声功率)计算得到的SNR值（dB为单位）
SNRpri =  -1.8124

参考如下：

1：https://www.it610.com/article/1297202824274321408.htm

2：https://ww2.mathworks.cn/help/comm/ug/awgn-channel.html?searchHighlight=AWGN%20Channel&s_tid=srchtitle

3:https://blog.csdn.net/Onelasttime/article/details/109712925

4:https://blog.csdn.net/dyp922/article/details/81197607?utm_medium=distribute.pc_relevant.none-task-blog-2%7Edefault%7EBlogCommendFromBaidu%7Edefault-3.control&depth_1-utm_source=distribute.pc_relevant.none-task-blog-2%7Edefault%7EBlogCommendFromBaidu%7Edefault-3.control