信号检测实验4误码率分析-参考答案.doc

实验四误码率的分析1、假定QPSK信号具有如下的星座图模式：1) 试利用二元数字通信系统的误码性能精确推导QPSK系统的误码率。2) 假设系统中的噪声是高斯白噪声，利用matlab对该系统在工作区间（信噪比010dB）下的误码性能进行仿真。简答：（1）、试利用二元数字通信系统的误码性能精确推导QPSK系统的误码率。解：令 表示每比特信号的能量 对于二元数字通信系统：二进制相移键控BPSK： 对于QPSK系统：其比特错误率等于BPSK的比特错误率，而误码率则是 当性噪比较高时，(2) 、说明：Eb = Energy-per-bitEs = Energy-per-symbol = nEb with n bits per symbolTb = Bit duration , Rb = Bit Rate, the bit transmission time Tb = 1/RbTs = Symbol durationN0 / 2 = Noise power spectral density (W/Hz)Pb = Probability of bit-errorPs = Probability of symbol-errorEb/N0 = The energy per bit to noise power spectral density ratio。It is a normalized signal-to-noise ratio (SNR) measure, also known as the SNR per bit.程序如下：clear allSNR_DB=0:1:12; %Signal-to-noise ratio gradually improvesum=1000000;data= randsrc(sum,2,0 1); %generate a 1000000*2 random matrix, using 0 1a1,b1=find(data(:,1)=0&data(:,2)=0); %returns the row and column indices of the evaluated expression which are TRUE.message(a1)=-1-j; % map 0 0 to 225a2,b2=find(data(:,1)=0&data(:,2)=1);message(a2)=-1+j; % map 0 1 to 135a3,b3=find(data(:,1)=1&data(:,2)=0);message(a3)=1-j; % map 1 0 to 275a4,b4=find(data(:,1)=1&data(:,2)=1);message(a4)=1+j;% map 0 0 to 45scatterplot(message)title(B点信号的星座图)A=1;Tb=1;Eb=A*A*Tb;P_signal=Eb/Tb;NO=Eb./(10.(SNR_DB/10); %SNR_DB=10.*log10(Eb./NO)P_noise=NO; %noise power 单边功率谱密度(N0)主要用在复数信号中，双边功率谱密度(N0/2)主要用在实信号中。sigma=sqrt(P_noise); for Eb_NO_id=1:length(sigma) noise1=sigma(Eb_NO_id)*randn(1,sum); noise2=sigma(Eb_NO_id)*randn(1,sum); receive=message+noise1+noise2*j; %previously unconsidered: how to add gaussian noise to the original signal resum=0; total=0; m1=find(angle(receive)0); %demodulate the 1 1 patter remessage(1,m1)=1+j; redata(m1,1)=1;redata(m1,2)=1; m2= find( angle(receive)pi/2&angle(receive)-pi&angle(receive)-pi/2&angle(receive)2000000 bits QPSK: 2bits per symbol total,ratio2=symerr(message,remessage); %Compute number of symbol errors and symbol error rate pe(Eb_NO_id)=total/sum; % Calculated according to the definitionendscatterplot(receive)title(C点信号的星座图)Pe=1-(1-1/2*erfc(sqrt(10.(SNR_DB/10)/2).2;Pbit=1/2*erfc(sqrt(10.(SNR_DB/10)/2);figure(3)semilogy(SNR_DB,pe,:s,SNR_DB,Pe,-*,SNR_DB,pbit,-o,SNR_DB,Pbit,:+)legend(QPSK仿真误码率,QPSK理论误码率,QPSK仿真误比特率,QPSK理论误比特率,1)xlabel(信噪比/dB)ylabel(概率P)grid on实验结果如下：（3） 若信号为16PSK，重做1。当信噪比较大时，仿真结果：