diff --git a/README.md b/README.md index 1249008..d8d59bf 100644 --- a/README.md +++ b/README.md @@ -58,29 +58,69 @@ For the assessment of BER, BPSK coding in the basic frequency range was used, ie Configure and run script ```bpsk_ber.m``` to generate BER vs SNR plots. #### Example Results -bpsk_ber_fig1 +bpsk_ber_fig1 ``` -BPSK simulation - BPSK - num of data bits to transfer through the channel: 1000000 - BER = -0.484644 for SNR = -10 - BER = -0.542406 for SNR = -8 - BER = -0.622411 for SNR = -6 - BER = -0.731174 for SNR = -4 - BER = -0.884889 for SNR = -2 - BER = -1.105961 for SNR = 0 - BER = -1.425159 for SNR = 2 - BER = -1.902257 for SNR = 4 - BER = -2.618704 for SNR = 6 - BER = -3.782516 for SNR = 8 - BER = -5.301030 for SNR = 10 +Input parameters: +Num of data bits to transfer through the channel = 5000 10000 50000 100000 500000 1e+06 5e+06 1e+07 +SNR (dB) = -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 + +* BPSK simulation * +Number of bits: 5000 +BER = -0.748119 for SNR = -4.0 +BER = -0.904482 for SNR = -2.0 +BER = -1.124939 for SNR = 0.0 +BER = -1.406714 for SNR = 2.0 +BER = -2.036212 for SNR = 4.0 +BER = -2.853872 for SNR = 6.0 +BER = -Inf for SNR = 8.0 +BER = -Inf for SNR = 10.0 +BER = -Inf for SNR = 12.0 + +* BPSK simulation * +Number of bits: 10000 +BER = -0.729787 for SNR = -4.0 +BER = -0.892451 for SNR = -2.0 +BER = -1.112946 for SNR = 0.0 +BER = -1.383000 for SNR = 2.0 +BER = -1.920819 for SNR = 4.0 +BER = -2.795880 for SNR = 6.0 +BER = -Inf for SNR = 8.0 +BER = -Inf for SNR = 10.0 +BER = -Inf for SNR = 12.0 + +... + +* BPSK simulation * +Number of bits: 5e+06 +BER = -0.729917 for SNR = -4.0 +BER = -0.884020 for SNR = -2.0 +BER = -1.104215 for SNR = 0.0 +BER = -1.425779 for SNR = 2.0 +BER = -1.901612 for SNR = 4.0 +BER = -2.622876 for SNR = 6.0 +BER = -3.719422 for SNR = 8.0 +BER = -5.522879 for SNR = 10.0 +BER = -Inf for SNR = 12.0 + +* BPSK simulation * +Number of bits: 1e+07 +BER = -0.729896 for SNR = -4.0 +BER = -0.884042 for SNR = -2.0 +BER = -1.105083 for SNR = 0.0 +BER = -1.427471 for SNR = 2.0 +BER = -1.902986 for SNR = 4.0 +BER = -2.618542 for SNR = 6.0 +BER = -3.728623 for SNR = 8.0 +BER = -5.376751 for SNR = 10.0 +BER = -Inf for SNR = 12.0 ``` ### Results Analysis The probability of incorrect bit detection (BER) is practically lost for a large SNR and is of the order of 1/N (1 bit in the sequence). All BER curves follow the theoretical BER curve with small deviations. -Therefore, the BER does not depend on the number of bits transmitted. + The minimum SNR for which BPSK has 1 bit error depends on the total transmitted bits, so that for a larger number of transmitted bits, the SNR must be higher for the signal to be correctly reconstructed. -For example. when transmitting 100 bits, it is enough for the SNR to exceed 4 dB so that there is no transmission error, while for the transmission of 100,000 bits, the SNR must exceed 8 dB. +For example: when transmitting 5 kb, it is enough for the SNR to exceed 6 dB so that there is no transmission error, while for the transmission of 5 Mb, the SNR must exceed 10 dB. [View BPSK system modeled and benchmarked against BER(SNR) on File Exchange](https://www.mathworks.com/matlabcentral/fileexchange/79224-bpsk-system-modeled-and-benchmarked-against-ber-snr)