Digital Communication

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1 Digital Communication (ECE4058) Electronics and Communication Engineering Hanyang University Haewoon Nam Lecture 15 1

2 Quadrature Phase Shift Keying Constellation plot BPSK QPSK Bit 0 Bit 1 00

3 M-ary Phase Shift Keying How to calculate it error rate (BER) and symol error rate (SER)? For BPSK, QPSK, M-ary PSK? How to draw a BER vs SNR curve? For other modulations? 3

4 Quadrature Amplitude Modulation 4

5 Mapping of Modulated Symols Mapping of digitally modulated waveforms onto constellation of signal points for BPSK The signal-space representation of BPSK is simple, involving a single asis function φ 1( t) = cos(πf ct) (7.44) T 5

6 Mapping of Modulated Symols Mapping of digitally modulated waveforms onto constellation of signal points for BFSK Two asis function each with different frequency φ ( t) = cos(πf 1 T 1 t ) (7.5) φ ( t) = cos(πf T t ) (7.53) 6

7 Simulations How can you perform simulations for BPSK, QPSK, etc? What functions do you need in Matla? How to create a transmitter, a receiver and AWGN channel? How to measure BER? Can you simplify the simulation compared to the actual system? 7

8 Binary Phase Shift Keying Antipodal signal 0 1 Constellation plot Binary data stream Non-return to zero level encoder Product modulator BPSK signal si ( t) = E T E T cos( πf t), c cos( πf t), c cos (a) BPSK modulator BPSK signal Product modulator Low-pass filter Sample at time Decision-making device Say 1, if the threshold is exceeded Say 0, otherwise cos Threshold () Coherent detector for BPSK, for the sampler, integer 0, 1,, 8

9 Quadrature Phase Shift Keying QPSK transmitter 9

10 Quadrature Phase Shift Keying QPSK receiver

11 BPSK Simulation Additive White Gaussian Noise (AWGN) environment Transmitter 1.5 Scatter plot + Receiver 1 Wireless channel 1.5 Scatter plot 0.5 Quadrature Quadrature In-Phase Received signal In-Phase : noise (AWGN) 11

12 BPSK Simulation Transmitter simulation Transmitter Binary data stream Non-return to zero level encoder BPSK signal AWGN channel simulation AWGN channel Real Gaussian Noise Source Imaginary Gaussian Noise Source + Complex Gaussian Noise 1

13 BPSK Simulation Receiver simulation Receiver Received signal Detection (Decision making) Non-return to zero level decoder Received inary data stream Overall simulation Binary data stream Transmitter + Receiver Received inary data stream Loop With varying SNR AWGN channel Comparison and BER calculation 13

14 Bit Error Proaility BER over Rayleigh fading channel (BPSK) Bit Error Rate AWGN no coding E /N (db)

15 BPSK Simulation num_its = ^7; % Transmitter tx_it_seq = randi(,1,num_its)-1; sym_seq = -sign(tx_it_seq - 0.5); % 0 -> 1, 1 -> -1 E = 5; % SNR = 0 db tx_sig = sqrt(e)*sym_seq; % Channel (AWGN) noise_sig = 1/sqrt()*(randn(1,num_its) + j*randn(1,num_its)); % Receiver rx_sig = tx_sig + noise_sig; rx_sig_re = real(rx_sig); rx_sym_seq = sign(rx_sig_re); rx_it_seq = -sign(rx_sym_seq-1); % BER cmpr_it = (tx_it_seq==rx_it_seq); it_err_pos = find(cmpr_it == 0); num_it_err = length(it_err_pos); er = num_it_err/num_its; 15

Digital Communication

Digital Communication (ECE4058) Electronics and Communication Engineering Hanyang University Haewoon Nam Lecture 1 1 Digital Band Pass Modulation echnique Digital and-pass modulation techniques Amplitude-shift