initial checkin, QPSK theory and experimental

git-svn-id: https://svn.code.sf.net/p/freetel/code@3029 01035d8c-6547-0410-b346-abe4f91aad63

diff --git a/codec2-dev/octave/hf_modem_curves.m b/codec2-dev/octave/hf_modem_curves.m
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+++ b/codec2-dev/octave/hf_modem_curves.m
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+% hf_modem_curves
+% David Rowe Feb 2017
+%
+% Ideal implementations of a bunch of different HF modems, used to
+% generate plots for a blog post.
+
+#{
+  [ ] ideal AWGN/HF curves
+  [ ] exp AWGN QPSK curves
+  [ ] exp AWGN DQPSK curves
+  [ ] exp HF channel model
+  [ ] with COHPSK frames
+#}
+
+1;
+
+% Gray coded QPSK modulation function
+
+function symbol = qpsk_mod(two_bits)
+    two_bits_decimal = sum(two_bits .* [2 1]); 
+    switch(two_bits_decimal)
+        case (0) symbol =  1;
+        case (1) symbol =  j;
+        case (2) symbol = -j;
+        case (3) symbol = -1;
+    endswitch
+endfunction
+
+
+% Gray coded QPSK demodulation function
+
+function two_bits = qpsk_demod(symbol)
+    bit0 = real(symbol*exp(j*pi/4)) < 0;
+    bit1 = imag(symbol*exp(j*pi/4)) < 0;
+    two_bits = [bit1 bit0];
+endfunction
+
+
+function sim_out = ber_test(sim_in)
+    bps     = 2; % two bits/symbol for QPSK
+
+    verbose = sim_in.verbose;
+    nbits   = sim_in.nbits;
+    nsymb   = nbits/bps;
+    EbNovec = sim_in.EbNovec;
+
+    for ne = 1:length(EbNovec)
+        EbNodB = EbNovec(ne);
+        EsNodB = EbNodB + 10*log10(bps);
+        EsNo = 10^(EsNodB/10);
+    
+        variance = 1/EsNo;
+
+        tx_bits = rand(1,nbits) > 0.5;
+        tx_symb = [];
+        for s=1:nsymb
+          atx_symb = qpsk_mod(tx_bits(2*s-1:2*s));
+          tx_symb = [tx_symb atx_symb];
+        end
+
+        % variance is noise power, which is divided equally between real and
+        % imag components of noise
+
+        noise = sqrt(variance*0.5)*(randn(1,nsymb) + j*randn(1,nsymb));
+        rx_symb = tx_symb + noise;
+
+        rx_bits = [];
+        for s=1:nsymb
+          two_bits = qpsk_demod(rx_symb(s));
+          rx_bits = [rx_bits two_bits];
+        end
+        
+        error_pattern = xor(tx_bits, rx_bits);
+        nerrors = sum(error_pattern);
+        bervec(ne) = nerrors/nbits;
+        if verbose
+          printf("EbNodB: %3.1f nerrors: %5d ber: %4.3f\n", EbNodB, nerrors, bervec(ne));
+        end
+    end
+
+    sim_out.bervec = bervec;
+endfunction
+
+% -------------------------------------------------------------
+
+function run_curves
+    sim_in.verbose = 1;
+    sim_in.nbits   = 100000;
+    sim_in.EbNovec = 0:7;
+
+    ber_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNovec/10)));
+    sim_qpsk = ber_test(sim_in);
+
+    figure(1); clf;
+    semilogy(sim_in.EbNovec, ber_theory,'r+-;QPSK AWGN theory;','markersize', 10, 'linewidth', 2)
+    hold on;
+    semilogy(sim_in.EbNovec, sim_qpsk.bervec,'g+-;QPSK AWGN simulated;','markersize', 10, 'linewidth', 2)
+    hold off;
+    xlabel('Eb/N0')
+    ylabel('BER')
+    grid("minor")
+    axis([min(sim_in.EbNovec) max(sim_in.EbNovec) 1E-3 1])
+
+endfunction
+
+% -------------------------------------------------------------
+
+more off;
+rand('seed',1); randn('seed', 1);
+run_curves