• Pseudo-Random Numbers

Because transmitters for this scheme are spatially distributed throughout an area (the cell), they cannot be synchronized and thus cannot be perfectly orthogonal.  CDMA uses sequences of pseudo-random (essentially random, but computer generated in a repeating pattern) bits as codes for the reverse link.  Several criteria are necessary for the selection of a set of pseudo-random numbers, which are carefully determined when designing a CDMA system.  In order to work in lieu of true orthogonal codes, these sequences must:

1)Contain approximately equal numbers of zeros and ones

2)Be approximately orthogonal to other codes

3)Be approximately orthogonal to themselves when delayed/shifted

4)Be easy to generate

• Gold Codes

Gold codes are specific sequences of pseudo-random numbers that can be generated using two feedback shift registers, and satisfy the above criteria.  A shift register is a digital logic structure where bits are shifted serially through a chain of memory cells.  A feedback shift register is a shift register structure that uses a modulo 2 addition on some of its bits to produce the bit fed into the input of the structure.  Most devices that use Gold codes use two of the structures, each adding a different subset of its bits to produce its feedback input.  The output of these two feedback shift registers is added (modulo 2) to produce the Gold code, which repeats with a sequence length less than that of the two sequences being added to produce it.  Different Gold codes can be produced by shifting the output of one of the feedback shift registers relative to the other; adding them produces a completely different sequence.

• Correlation and Orthogonality

The criteria for desirable pseudo-random sequences specify much about “approximate” orthogonality, but the meaning of such a statement is not necessarily intuitive.  A degree of orthogonality between two sequences can be measured using a statistical tool, cross-correlation.  A value of zero indicates actual orthogonality; our measurements are normalized so that a value of one indicates identicality, the complete lack of orthogonality.  To select Gold codes, cross-correlation of two candidates is calculated for all possible shifts, or phases, of the two codes, to account for all possible reception patterns that could arise with two distinct transmitters each using one of the codes to transmit to the same tower.  A “good” set of codes will have magnitudes(positive or negative) of cross-correlation much less than one for all shifts.  In an urban environment, a tower will frequently receive multiple copies of the same signal delayed because of different path lengths from the signal reflecting off of buildings.  In order to minimize interference from the delayed signals, a “good” code will have low values of autocorrelation (cross-correlation with itself), for any shift other than zero, where it is by definition one.  The plot below shows the correlation data for two of the codes used in our experiment; these codes are considered “good” for the code length that we used (21 bits). ©2001 Kyle Bryson, Alison Chen, and Allen Wan