1 function passband(rolloff, M, numSymbs)
2 %% Set defaults for inputs
14 %% https://www.mathworks.com/help/comm/examples/passband-modulation-with-adjacent-channel-interference.html
15 Rsym = 1e6; % symbol rate (sym/sec)
17 span = 6; % filter span
18 sps = 4; % samples per symbol
20 txFilter = comm.RaisedCosineTransmitFilter...
21 ('Shape', 'Square root', ...
22 'RolloffFactor', rolloff, ...
23 'FilterSpanInSymbols', span, ...
24 'OutputSamplesPerSymbol', sps);
25 rxFilter = comm.RaisedCosineReceiveFilter...
26 ('Shape', 'Square root', ...
27 'RolloffFactor', rolloff, ...
28 'FilterSpanInSymbols', span, ...
29 'InputSamplesPerSymbol', sps, ...
30 'DecimationFactor', 1);
32 fs = Rsym * sps; % sampling freq (Hz)
34 t = (0 : 1 / fs : numSymbs / Rsym + (1.5 * span * sps - 1) / fs)';
38 EbN0 = 10 .^ (EbN0_db ./ 10);
44 EsN0 = EbN0 .* log2(M);
45 EsN0_db = 10 .* log10(EsN0);
47 plotlen = length(EbN0);
49 ber = zeros(1, plotlen);
54 data = randi([0 M - 1], numSymbs, 1);
55 modData = pskmod(data, M, 0, 'gray');
57 xBaseband = txFilter([modData; zeros(span, 1)]);
60 %fc = 2.5e6; % Carrier freq (Hz)
61 %carrier = sqrt(2) * exp(j * 2 * pi * fc * t);
63 %xPassbandIdeal = normalizeEnergy...
64 % (real(xBaseband .* carrier(1:length(xBaseband))), numSymbs, 1);
66 %txLOFreq = [2.49e6, 2.5e6, 2.51e6];
67 %%txLOEnergy = [0.05, 0.9, 0.05];
68 %txLOEnergy = [0 1 0];
72 carrier = zeros(length(t), 1);
73 for i = 1 : length(txLOFreq)
74 carrier = carrier + ...
75 sqrt(2 * txLOEnergy(i)) * exp(j * 2 * pi * txLOFreq(i) * t);
78 xPassband = normalizeEnergy...
79 (xBaseband .* carrier(1:length(xBaseband)), numSymbs, 1);
82 snr = EbN0_db(i) + 10 * log10(log2(M)) - 10 * log10(sps); % why sps?
83 noiseEnergy = 10 ^ (-snr / 10);
85 yPassband = awgn(xPassband, snr, 'measured');
87 rBaseband = rxFilter([yPassband .* conj(carrier(1:length(yPassband))); zeros(span * sps, 1)]);
88 %% truncate filter transients
89 rBaseband = rBaseband(span * sps / 2 + 1 : end);
91 rBaseband = normalizeEnergy(rBaseband, numSymbs, 1 + noiseEnergy);
93 rSampled = rBaseband(sps*span/2+1:sps:(numSymbs + span/2) * sps);
95 demodData = pskdemod(rSampled, M, 0, 'gray');
96 [bitErrors, ber(i)] = biterr(data, demodData);
103 %% Plot simulated results
104 semilogy(EbN0_db, ber, 'r', 'LineWidth', 2);
107 %% Plot theoretical curve
108 %% BPSK: bit error when noise Nr > sqrt(Eb)
110 %% = Pr(Z > sqrt(Eb) / sqrt(N0/2))
112 %% QPSK = 2 BPSKs, one real and one imaginary, each with one bit
113 %% so BER is the same as BPSK (assuming Gray code)
115 ber_th = qfunc(sqrt(2 * EbN0));
116 semilogy(EbN0_db, ber_th, 'b', 'LineWidth', 1);
117 legend('Simulated RRC', 'Discrete');
119 %% Approximation: J.G. Proakis and M. Salehi, 2000, Contemporary
120 %% Communication Systems using MATLAB (Equations
121 %% 7.3.18 and 7.3.19), Brooks/Cole.
122 ber_ap = 2 * qfunc(sqrt(EbN0 * log2(M) * 2) * sin(pi / M)) / log2(M);
123 semilogy(EbN0_db, ber_ap, 'b', 'LineWidth', 1);
124 legend('Simulated RRC', 'Discrete');
127 title(strcat(num2str(M), '-PSK RRC with Gray code'));
129 xlabel('$E_b/N_0$ (dB)');
133 %saveas(gcf, strcat('BER_SNR_', num2str(M), 'PSK_', num2str(numSymbs), ...
136 %scatterplot(rxFilt);
137 %eyediagram(rxFilt, sps);
142 function y = normalizeEnergy(x, numSymbs, e)
143 energy = sum(abs(x) .^ 2) / numSymbs;
144 y = x * sqrt(e / energy);