%?SNR_start=0;
%?SNR_delta=1;
%?SNR_stop=40;
%?BER_stop=0.00001;
%?sigma=0.5;
%?
%????%?Choose?a?file?to?save?the?results?into.
%?????filename?=?[‘results_‘num2str（SNR_start）‘.mat‘];
%?????%?Doing?the?simulation?frame-by-frame?rather?than?bit-by-bit?speeds?it?up.?This?is?because?we?can?use?vector?operations?instead?of?longer?loops.
%?????frame_length?=?10000;
%?????%?Setup?the?SNR?for?the?first?iteration?of?the?loop.
%?????SNR_count?=?1;
%?????SNR?=?SNR_start;
%?????BER?=?1;
%?
%?????%?Loop?until?the?job?is?killed?or?until?the?SNR?or?BER?target?is?reached.
%?????while?SNR?<=?SNR_stop?&&?BER?>=?BER_stop
%?
%?????????%?Convert?from?SNR?（in?dB）?to?noise?power?spectral?density.
%??????????N0?=?1/（10^（（SNR+3.0103）/10））;
%?????????
%?????????%?Counters?to?store?the?number?of?errors?and?bits?simulated?so?far.
%?????????error_count=0;
%?????????bit_count=0;
%????????
%?????????%?Keep?going?until?enough?errors?have?been?observed.?This?runs?the?simulation?only?as?long?as?is?required?to?keep?the?BER?vs?SNR?curve?smooth.
%?????????while?error_count?%?%--------------------------------------------------------------------------????????????
%?
%?%?BPSK?Generate?10000?symbols?each?contain?2?bits
%?%?rand（‘seed‘1）;
%?realpart=round（rand（1frame_length））;
%?imagpart=round（rand（1frame_length））;
%?a=2^（-1/2）;
%?xk=2*a*（（realpart-0.5）+i*（imagpart-0.5））;
%?
%?%?passing?channel?
%?
%?xt=xk;???????????%?no?phase?and?amplitude?distortion?
%?
%?
%?%?additive?white?Gaussian?noise?（AWGN）
%?snr=1/N0;
%?Ls?=?length（xt）;
%?sigma_x=std（xt）;
%?sigma_n?=?1/sqrt（2*snr）;
%?noise=sigma_x*sigma_n*（randn（1Ls）+i*randn（1Ls））;
%?
%?%?fading?channel
%?channel?=?sqrt（sigma）*（randn（1Ls）+i*randn（1Ls））;
%?
%?xt_addnoise?=?xt.*（channel）?+?noise;
%?
%?%?decode?the?signal
%?xk_hat=xt_addnoise;?????%?down-sample?the?signal?
%?
%?
%?b_1hat=real（xk_hat）>0;
%?b_2hat=imag（xk_hat）>0;
%?
%?error_count=（sum（b_1hat~=realpart）+sum（b_2hat~=imagpart））+error_count;
%?bit_count=bit_count+frame_length*2;
%?
%?%?BER=（sum（b_1hat~=realpart）+sum（b_2hat~=imagpart））/20000
%?????????????
%?????????end
%?????????
%?????????%?Calculate?the?BER.
%?????????BER?=?error_count/bit_count;
%?????????
%?????????%?Store?the?SNR?and?BER?in?a?matrix?and?display?it.
%?????????results（SNR_count1）?=?SNR;
%?????????results（SNR_count2）?=?BER
%?????????
%?????????%?Save?the?results?into?binary?files.?This?avoids?the?loss?of?precision?that?is?associated?with?ASCII?files.
%?????????save（filename?‘results‘?‘-MAT‘）;
%???semilogy（results（:1）results（:2）‘bv-‘）;
%??????????????
%?????????xlabel（‘Eb/No?（in?dB）‘）
%?????????if?BER_stop?~=?0?
%?????????????ylim（[BER_stop1]）;
%?????????end
%?????????if?SNR_stop?~=?inf
%?????????????xlim（[SNR_start?SNR_stop]）;
%?????????end
%?????????
%?????????%?Setup?the?SNR?for?the?next?iteration?of?the?loop.
%?????????SNR?=?SNR?+?SNR_delta;
%?????????SNR_count?=?SNR_count?+?1;
%?????end
%?results1=res