Added function that finds the start time offset based on the cyclic prefix

matlab/updated_scripts/find_sto_cp.m

@@ -0,0 +1,65 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Find the start time offset based on the cyclic prefix
+%
+% This method is immune to the issues that plague the ZC sequences (frequency offset causes a time shift in the
+% correlation results)
+%
+% It's best to provide this function an upsampled copy of the burst to help fix any fractional time offset that might be
+% present
+%
+% @param samples Complex IQ samples that make up the full burst
+% @param sample_rate Sample rate (in Hz) of the provided samples
+% @return start_offset Sample index that the burst starts at (first sample of the first cyclic prefix)
+function [start_offset] = find_sto_cp(samples, sample_rate)
+    [long_cp_len, short_cp_len] = get_cyclic_prefix_lengths(sample_rate);
+    fft_size = get_fft_size(sample_rate);
+    cyclic_prefix_length_schedule = [...
+        long_cp_len, ...
+        short_cp_len, ...
+        short_cp_len, ...
+        short_cp_len, ...
+        short_cp_len, ...
+        short_cp_len, ...
+        short_cp_len, ...
+        short_cp_len, ...
+        long_cp_len];
+    num_ofdm_symbols = length(cyclic_prefix_length_schedule);
+
+    full_burst_len = sum(cyclic_prefix_length_schedule) + (fft_size * num_ofdm_symbols);
+    num_tests = length(samples) - full_burst_len;
+    scores_cp_sto = zeros(1, num_tests);
+
+    for idx=1:num_tests
+        offset = idx;
+        scores = zeros(1, num_ofdm_symbols);
+    
+        % Extract and correlate the samples that each cyclic prefix is expected
+        % to be at
+        for cp_idx=1:num_ofdm_symbols
+            cp_len = cyclic_prefix_length_schedule(cp_idx);
+    
+            % Extract the full OFDM symbol including cyclic prefix
+            window = samples(offset:offset + fft_size + cp_len - 1);
+    
+            % Extract the cyclic prefix and the final samples of the symbol
+            left = window(1:cp_len);
+            right = window(end - cp_len + 1:end);
+    
+            % Correlate the two windows
+            scores(cp_idx) = abs(xcorr(left, right, 0, 'normalized'));
+    
+            % Move the sample pointer forward by the full symbol size
+            offset = offset + cp_len + fft_size;
+        end
+    
+        % In the real DroneID the first OFDM symbol needs to be ignored since
+        % it isn't always present.  So, just average the correlation scores of
+        % all but the first element
+        scores_cp_sto(idx) = sum(scores(2:end)) / (length(scores) - 1);
+
+    end
+
+    % Find the index of the highest score
+    [~, start_offset] = max(scores_cp_sto);
+end
+