From 7fa0fc4988f88c6f608e86c003e204171d892fa3 Mon Sep 17 00:00:00 2001
From: proto17 <dmp250net@gmail.com>
Date: Wed, 18 May 2022 23:40:07 -0400
Subject: [PATCH] Create est_integer_freq_offset.m

---
 .../updated_scripts/est_integer_freq_offset.m | 51 +++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 matlab/updated_scripts/est_integer_freq_offset.m

diff --git a/matlab/updated_scripts/est_integer_freq_offset.m b/matlab/updated_scripts/est_integer_freq_offset.m
new file mode 100644
index 0000000..f13cf77
--- /dev/null
+++ b/matlab/updated_scripts/est_integer_freq_offset.m
@@ -0,0 +1,51 @@
+% Estimates the integer frequency offset using the time domain samples of
+% the first ZC sequence (root index 600)
+%
+% @param received_zc_td Time domain of the received ZC sequence with no
+%                       cyclic prefix (should be row vector)
+% @param sample_rate Sample rate of the samples in Hz
+% @param max_carrier_offset How much integer frequency offset to search for
+%                           (must be positive non-zero value)
+% @return integer_offset_hz Best estimate for the integer frequency offset
+%                           in Hz
+function [integer_offset_hz] = est_integer_freq_offset(received_zc_td, sample_rate, max_carrier_offset)
+    fft_size = get_fft_size(sample_rate);
+    
+    assert(isrow(received_zc_td), "ZC time domain samples must be row vector");
+    assert(length(received_zc_td) == fft_size, "ZC time domain samples must be FFT samples wide");
+    assert(isnumeric(sample_rate) && sample_rate > 0, "Sample rate must be positive and non-zero");
+    assert(isnumeric(max_carrier_offset) && max_carrier_offset > 0, "Max carrier offset must be positive and non-zero");
+    
+    % Calculate all of the cyclic shifts that will be done to search for
+    % the integer frequency offset value
+    shift_range = -max_carrier_offset:1:max_carrier_offset;
+    
+    % Allocate storage for the correlation scores from each shift
+    scores = zeros(1, length(shift_range));
+    
+    % Move the ZC sequence to the frequency domain
+    zc_fd = fft(received_zc_td);
+
+    for idx=1:length(shift_range)
+        % Circularly shift the FFT
+        zc_fd_shifted = circshift(zc_fd, shift_range(idx));
+        
+        % Take the upper and lower `(fft_size / 2) - 1` samples 
+        left = zc_fd_shifted(1:(fft_size / 2) - 1);
+        right = zc_fd_shifted((fft_size / 2) + 2:end);
+        
+        % Correlate the lower samples with the mirror of the upper samples
+        scores(idx) = xcorr(left, fliplr(right), 0);
+    end
+    
+    % Find the index of the max score
+    [~, index] = max(abs(scores));
+    
+    % Calculate the number of Hz between each FFT bin
+    carrier_spacing = sample_rate / fft_size;
+    
+    % Get how many carriers the best score was shifted by and multiply that
+    % value by the carrier spacing to get the integer frequency offset
+    integer_offset_hz = shift_range(index) * carrier_spacing;
+end
+