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diff --git a/octave/qpsk.m b/octave/qpsk.m
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+% qpsk.m
+%
+% David Rowe Sep 2015
+%
+% Octave functions to implement a QPSK modem
+
+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
+
+
+% Inserts pilot symbols a frame of symbols.  The pilot symbols are
+% spread evenly throughout the input frame.
+
+function frameout = insert_pilots(framein, pilots, Npilotstep)
+
+    lpilots = length(pilots);
+    lframein = length(framein);
+    frameout = zeros(1, lframein + lpilots);
+
+    pin = 1; pout = 1; ppilots = 1;
+    while (lpilots)
+        %printf("pin %d pout %d ppilots %d lpilots %d\n", pin, pout, ppilots, lpilots);
+        frameout(pout:pout+Npilotstep-1) = framein(pin:pin+Npilotstep-1);
+        pin  += Npilotstep; 
+        pout += Npilotstep;
+        frameout(pout:pout) = pilots(ppilots);
+        ppilots++;
+        pout++;
+        lpilots--;
+    end
+endfunction
+
+
+% Removes the pilots symbols from a frame of symbols.
+
+function frameout = remove_pilots(framein, pilots, Npilotstep)
+
+    frameout = [];
+    lpilots = length(pilots);
+
+    pin = 1; pout = 1;
+    while (lpilots)
+        %printf("pin %d pout %d lpilots %d  ", pin, pout, lpilots);
+        %printf("pin+spacing-1 %d lvd %d lframein: %d\n", pin+spacing-1, lvd, length(framein));
+        frameout(pout:pout+Npilotstep-1) = framein(pin:pin+Npilotstep-1);
+        pin  += Npilotstep+1;
+        pout += Npilotstep;
+        lpilots--;
+    end
+
+endfunction
+
+
+% Estimate and correct phase offset using a window of Np pilots around
+% current symbol
+
+function symbpilot_rx = correct_phase_offset(aqpsk, symbpilot_rx)
+  rx_pilot_buf = aqpsk.rx_pilot_buf;
+  Npilotstep   = aqpsk.Npilotstep;
+  Nsymb        = aqpsk.Nsymb;
+
+  for ns=1:Npilotstep+1:Nsymb
+
+    % update buffer of recent pilots, note we need past ones
+
+    rx_pilot_buf(1) = rx_pilot_buf(2);
+    next_pilot_index = ceil(ns/(Npilotstep+1))*(Npilotstep+1);
+    rx_pilot_buf(2) = symbpilot_rx(next_pilot_index);
+
+    % average pilot symbols to get estimate of phase
+
+    phase_est = angle(sum(rx_pilot_buf));
+
+    %printf("next_pilot_index: %d phase_est: %f\n", next_pilot_index, phase_est);
+
+    % now correct the phase of each symbol
+
+    for s=ns:ns+Npilotstep
+      symbpilot_rx(s) *= exp(-j*phase_est);     
+    end
+  end
+
+  aqpsk.rx_pilot_buf = rx_pilot_buf;
+endfunction
+
+
+% builds up a sparse QPSK modulated version version of the UW for use
+% in UW sync at the rx
+
+function mod_uw = build_mod_uw(uw, spacing)
+    luw = length(uw);
+
+    mod_uw = [];
+
+    pout = 1; puw = 1;
+    while (luw)
+        %printf("pin %d pout %d puw %d luw %d\n", pin, pout, puw, luw);
+        pout += spacing/2;
+        mod_uw(pout) = qpsk_mod(uw(puw:puw+1));
+        puw += 2;
+        pout += 1;
+        luw -= 2;
+    end
+endfunction
+
+
+% Uses the UW to determine when we have a full codeword ready for decoding
+
+function [found_uw corr] = look_for_uw(mem_rx_symbols, mod_uw)
+    sparse_mem_rx_symbols = mem_rx_symbols(find(mod_uw));
+
+    % correlate with ref UW
+
+    num = (mem_rx_symbols * mod_uw') .^ 2;
+    den = (sparse_mem_rx_symbols * sparse_mem_rx_symbols') * (mod_uw * mod_uw');
+    
+    corr = abs(num/(den+1E-6));
+    found_uw = corr > 0.8;
+endfunction
+