How Close Can Destinations Sit? Minimum Phase Separation for Reliable Addressing

Destinations that sit too close together on the phase circle will be confused with one another. This paper derives the minimum separation for reliable addressing. With Gaussian arrival error of standard deviation sigma and nearest-neighbour decisions, keeping the misdelivery probability at or below one in a million requires a separation of at least 2 sigma x 4.7534. For sigma = 0.01 rad the required separation is 0.0951 rad, allowing 66 addresses per turn; for sigma = 0.02 rad the separation is 0.1901 rad and 33 addresses; for sigma equal to the full 0.0667 rad budget the separation grows to 0.6341 rad and only 9 addresses fit. At a fixed separation of 0.2 rad, misdelivery probability ranges from effectively zero at the smallest sigma to 0.0669 at the largest. Addressing capacity is therefore bought directly with arrival precision. Computed; not measured. SIMULATED, NOT MEASURED.