Why do we need to write the noise as randn(2,1)./sqrt(2*SNR) instead of randn(1,1)/sqrt(2)?

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yang-En Hsiao 2019-4-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/457635-why-do-we-need-to-write-the-noise-as-randn-2-1-sqrt-2-snr-instead-of-randn-1-1-sqrt-2

编辑： yang-En Hsiao 2019-4-21

I saw this code, about the error probability of on/off signal ,on the internet

Ts=10^4;
SNR_dB=[-3 0 3 6 9];
Ne=zeros(1,length(SNR_dB));
for i=1:length(SNR_dB)
    SNR=10^(SNR_dB(i)/10);
    for t=1:Ts
        s=((sign(rand()-0.5))+1)/2;%create the "on"signal or "off" signal ."on"signal=1,"off" signal=0
        r=randn(2,1)./sqrt(2.*SNR);%it seems that it is noise
        if (s+r)>0.5
            s_hat=1;
        else
            s_hat=0;
        end
        if abs(s_hat-s)>0
            Ne(i)=Ne(i)+1;
        end
        y=Ne./Ts;
    end
end
Pe=zeros(1,5);
for i=1:5
    SNR=10^(SNR_dB(i)/10);
    Pe(i)=erfc(sqrt(SNR/2)/(2^0.5))/2;
end
semilogy(SNR_dB,y,'-r',SNR_dB,Pe,'-k')