Simulacin de un Sistema de Comunicacion Digital Bit
Simulación de un Sistema de Comunicacion Digital Bit Error Rate (BER) for BPSK Modulation in an AWGN Channe Cesar A. Azurdia Meza. Principios de Comunicaciones EL 4005
General Overview l Theoretical Error Probability for BPSK l Monte Carlo Simulation: Bit Error Rate (BER) for BPSK Modulation l Simulation/Analytical Results l Conclusion 2
Sistema de Comunicacion Basico AWGN N TX S + R Channel Model R=S+N Detection Performance: l Detección Correcta l S = S* l Detección Erronea l S ≠ S* RX Detection S*
BPSK Modulation over AWGN Channels ES Energia por simbolo
BPSK Modulation over AWGN Channels Gaussian Noise 0
BPSK Modulation over AWGN Channels Received signal distribution given 0 transmitted
BPSK Modulation over AWGN Channels Error Calculation given Symmetry of Gaussian Distribution Let 0 transmitted
BPSK Modulation over AWGN Channels Received signal distribution given 0 transmitted
BPSK Modulation over AWGN Channels Error Calculation given Let 0 transmitted
BPSK Modulation over AWGN Channels Signal Power & Symbol Error Performance 0
BPSK Modulation over AWGN Channels Signal Power & Symbol Error Performance 0
BER of PSK over AWGN Channels Notes: l Define N 0 Total Noise Power l N 0/2 Noise Power over Cosine axis, i. e. , σ2=N 0/2 l Each symbol corresponds to a single bit l Eb = ES l Pb = Pe
General Overview l Theoretical Error Probability for BPSK l Monte Carlo Simulation: Bit Error Rate (BER) for BPSK Modulation l Simulation/Analytical Results l Conclusion 13
Bit Error Rate (BER) for BPSK modulation l Secuencia binaria de 1/0 s representada por niveles de energía l La secuencia de bits es alterada por ruido AGWN § Los valores del ruido n provienen de una distribución probabilística Gaussiana 14
Computing the error probability: BPSK l La señal recibida es dada por l The conditional probability distribution function of y for the two cases is 15
Computing the error probability: BPSK 16
Detection of the Received Signal l Si asumimos que S 0 y S 1 tienen la misma probabilidad de ocurrencia: l y > 0 el receptor asume que fue transmitido un 1 l y < 0 el receptor asume que fue transmitido un -1 l The total probability of error for BPSK modulation is given as 17
Simulation Model l Generation of random BPSK modulated symbols +1′s and 1′s. (Baseband signals) l Addition of AGWN noise l Demodulation of the received symbol based on the location in the constellation. l Counting the number of errors l Repeating the same for multiple Eb/No value. 19
System Parameters l num_bit=100000; %Signal length l max_run=20; %Maximum number of iterations for a single SNR l Eb=1; %Bit energy l SNRd. B=0: 1: 9; %Signal to Noise Ratio (in d. B) l SNR=10. ^(SNRd. B/10); 20
Monte Carlo Simulation 21
Analytical BER: BPSK l Plot of Monte Carlo Simulation and Theoretical curves 22
General Overview l Theoretical Error Probability for BPSK l Monte Carlo Simulation: Bit Error Rate (BER) for BPSK Modulation l Simulation/Analytical Results l Conclusion 23
Simulation/Analytical Results 24
General Overview l Theoretical Error Probability for BPSK l Monte Carlo Simulation: Bit Error Rate (BER) for BPSK Modulation l Simulation/Analytical Results l Conclusion 25
Conclusion l Each modulation scheme and channel model has its own error probability expression. l Theoretical and simulation curves converge to the same values as the number of random data points increases. l For the error probability to decrease, we need to increase the energy of the transmitted symbol. 26
¿Preguntas o Dudas? 27
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