How Auto Correlation in CDMA


Auto-correlation is simply a comparison of a signal against itself. For a digital sequence, such as the short codes used in EIA/TIA-95-B, this comparison is a measure of the number of bits that match relative to the number of bits that do not match.

Good pseudo-random patterns (such as the short codes) are designed to have near perfect auto-correlation when time aligned and have very weak auto-correlation at all other time offsets. In other words, the short codes are designed to match when aligned and have a near zero match (equal number of matches and mismatches) at all other time alignments.

The auto-correlation of a good pseudo-random digital sequence against itself verses time offset. You can see that there is strong correlation with zero offset, and that at all other offsets, the net correlation is near zero. This property makes finding the short code at a given PN Offset easy.

  • Is a Comparison of a Signal Against Itself
  • Good Pseudo-Random Patterns Have:
  1. Strong Correlation at Zero Time Offset
  2. Weak Correlation at Other Time Offsets

Short Code Correlation

The short codes are designed to have strong auto-correlation at zero time offset and weak auto-correlation at other time offsets. But what happens to the auto-correlation properties when there are many short codes with different PN Offsets present at the same time? This is the condition present in a real, working EIT/TIA-95-B network.

The auto-correlation of a short codes in the presence of 17 dB of added white noise. White noise can be used since another property of the short codes is that they appear as white noise interference to receivers looking for different PN Offset short codes. Even with this much added noise, the auto-correlation at zero offset is strong.

At other offsets, the net auto-correlation is not zero, but is still relatively weak compared to the zero offset auto-correlation. These properties of the short codes allow CDMA receivers to quickly acquire the desired PN Offset signal even in the presence of large amounts of interference.

Short Codes are Designed to Have:

  • Strong Auto-Correlation at Zero Time Offset
  • Weak Auto-Correlation at Other Offsets
  • Good Auto-Correlation in Very Poor Signal-to-Noise Ratio Environments
  • Allows Fast Acquisition in Real World Environment