Correlators and Matched Filters
Application: Finding the value of the correlation function between the transmitted signal symbol s(t) and the received signal r(t) is the optimum way of measuring or determining the signal symbol in wideband uniformly distributed noise or interference. Since these coded symbols are used to determine the bits that carry the message, correlation is part of the optimum way of recovering the IS-95 message.
The coded symbols s(t) in IS-95 are the Walsh words which contain 64 Walsh chips. The correlators or matched filters in the mobile receiver correlate the received signal r(t) with the Walsh word s(t) assigned to that mobile for that call. The base station receiver uses a Fast Walsh Transform (FWT) which correlated the received signal r(t) with all 64 Walsh words to determine which one was sent from the mobile.
Correlators and Matched Filters
Example: A Walsh word s(t) with 8 Walsh chips is given by +1-1+1-1+1-1+1-1 and a second Walsh word is +1-1-1+1+1-1-1+1. Assume, r(t) equals the sum of these Walsh words . Then r(t) equals +2-200+2-200. Assuming one sample per Walsh chip, M equals 8 and the correlation of s(t) with r(t) at t equal to zero, indicating the proper time for the symbol measurement, equals
Rsr(0) ˜ M-1?s(mD)r(mD) =(1/8)[(+1)(+2) + (-1)(-2) + (+1)(0) (1)
+(-1)(0) + (+1)(+2) + (-1)(-2) + (+1)(0) + (-1)(0)] = 1
The correlation of s(t) with this r(t) equals the correlation of s(t) with itself. The correlation contribution from the second Walsh word is zero.
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