Digital Communication (ECE4058) Electronics and Communication Engineering Hanyang University Haewoon Nam Lecture 15 1
Quadrature Phase Shift Keying Constellation plot BPSK QPSK 01 11 Bit 0 Bit 1 00
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
Quadrature Amplitude Modulation 4
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
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
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
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
Quadrature Phase Shift Keying QPSK transmitter 9
Quadrature Phase Shift Keying QPSK receiver
BPSK Simulation Additive White Gaussian Noise (AWGN) environment Transmitter 1.5 Scatter plot + Receiver 1 Wireless channel 1.5 Scatter plot 0.5 Quadrature 0 1 0.5-0.5-1 Quadrature 0-0.5-1.5-1.5-1 -0.5 0 0.5 1 1.5 In-Phase Received signal -1-1.5-1.5-1 -0.5 0 0.5 1 1.5 In-Phase : noise (AWGN) 11
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
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
Bit Error Proaility BER over Rayleigh fading channel (BPSK) Bit Error Rate 0-1 - -3-4 -5 AWGN no coding -6 0 4 6 8 1 E /N (db) 14 16 18 0 0 14
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