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

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