Search Window Offset ((hot)) [PREMIUM – SUMMARY]

For a data sequence ( D[0, N-1] ) and a reference index ( R ), a search window ( W ) of length ( L ) starting at offset ( O ) is:

[ K = \left\lceil \fracS - L\Delta \right\rceil + 1 ] search window offset

If the target signal is uniformly distributed within the search space, the probability ( P_detect ) that the target lies within a specific window starting at offset ( O ) is: For a data sequence ( D[0, N-1] )

Start offset = 0 → Window [0, 499] Next offset = 400 → Window [400, 899] Next offset = 800 → Window [800, 1299] (wraps) Total 4 windows to cover ~1535 chips. For a data sequence ( D[0

[ P_detect(O) = \fracLS \quad \text(for random target position) ]