Create cyclic_prefix_sto_test.m

matlab/updated_scripts/cyclic_prefix_sto_test.m

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+clear all;
+
+% This script is meant to test using the cyclic prefix to find the starting time offset (STO) of a
+% DroneID burst
+
+%% Parameters
+sample_rate = 15.36e6;
+fft_size = get_fft_size(sample_rate);
+[long_cp_len, short_cp_len] = get_cyclic_prefix_lengths(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_data_carriers = 600;
+left_guards = (fft_size / 2) - (num_data_carriers / 2);
+right_guards = left_guards - 1;
+num_ofdm_symbols = 9;
+carrier_spacing = sample_rate / fft_size;
+zero_padding_count = 100;
+modulation_order = 4;
+
+% User definable parameters
+integer_freq_offset = -58;
+snr = 0;
+enable_plots = 1;
+
+%% Create Time Domain Samples
+modulator = comm.OFDMModulator( ...
+    "FFTLength",            fft_size, ...
+    "NumGuardBandCarriers", [left_guards; right_guards], ...
+    "CyclicPrefixLength",   cyclic_prefix_length_schedule, ...
+    "NumSymbols",           num_ofdm_symbols, ...
+    "InsertDCNull",         true);
+
+% Generate the PSK that will be used in the data carriers of each OFDM sym
+data_carriers = pskmod(...
+    randi([0, log2(modulation_order)], num_data_carriers, num_ofdm_symbols), ...
+    modulation_order);
+
+% Create the time domain samples and convert to a row vector
+samples = modulator(data_carriers);
+samples = reshape(samples, 1, []);
+
+% Add in zeros to the left and right
+samples = [zeros(1, zero_padding_count), samples, zeros(1, zero_padding_count)];
+
+if (enable_plots)
+    figure(1);
+    plot(10 * log10(abs(samples).^2));
+    title('Original Time Domain');
+end
+
+%% Apply Integer Frequency Offset
+int_freq_offset_hz = integer_freq_offset * carrier_spacing;
+int_offset_vec = exp(1j * 2 * pi * int_freq_offset_hz / sample_rate * [0:(length(samples)-1)]);
+
+samples = samples .* int_offset_vec;
+
+%% Add Noise
+samples = awgn(samples, snr, 'measured');
+
+if (enable_plots)
+    figure(2);
+    plot(10 * log10(abs(samples).^2));
+    title('Samples With Noise & Int Freq Offset');
+end
+
+%% Find STO with Cyclic Prefix
+
+% How far from the first sample to search for the STO
+num_offsets = zero_padding_count * 1.5;
+scores_cp_sto = zeros(1, num_offsets);
+
+for idx=1:length(scores_cp_sto)
+    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
+
+if (enable_plots)
+    figure(3);
+    plot(scores_cp_sto);
+    title('STO Scores (Cyclic Prefix)')
+end
+
+% Find the index of the highest score
+[~, sto_est_cp] = max(scores_cp_sto);
+fprintf("True offset: %d, estimated offset: %d\n", zero_padding_count + 1, sto_est_cp);
+
+if (enable_plots)
+    figure(4);
+    plot(10 * log10(abs(fftshift(fft(samples))).^2));
+    title('FFT of Noisy Signal');
+end
+
+% XCorr for ZC -> Extract Burst -> CP STO -> Coarse CFO -> Integer CFO -> Equalization