## JPL's Wireless Communication Reference Website## Chapter: Analog and Digital Transmission |

In Direct-Sequence CDMA, the user signal is multiplied by a pseudo-noise code sequence of high bandwidth. This code sequence is also called the chip sequence. The resulting coded signal is transmitted over the radio channel.

Figure: User signal and code are multiplied to generate the coded transmit signal.

**Autocorrelation**- The (normalized) autocorrelation of the spreading waveform
*p(t)*is defined by1

where*inf**R*(t) = - int_{c}*p*(*t*)*p*(*t*+ t)*dt*T 0*p(t)*is the transmit waveform of the code,*T = N*is the code period time and t represents a time shift._{c}T_{c} **Partial Autocorrelation**- If a bit transition occurs (from +1 to -1 or vice versa), the interference from a delay CDMA signal consists of two fractions of a bit duration. The Partial Autocorrelation is similar to the above formula, but integrated only of a portion of the bit duration.
**Crosscorrelation**- Different signals have different spreading codes. The crosscorrelation between two codes
*i*and*j*is1

which equals the autocorrelation if*inf**R*(t) = - int_{c}*p*T 0_{i}(t) p_{j}(t + t) dt*i = j*.

Popular code sequences used in spread-spectrum transmission are

- Maximum Length sequences
- Walsh Hadamard sequences
- Gold codes, and
- Kasami codes.

The user capacity of a synchronous CDMA system, in which the various user signals
exhibit no time offsets when they arrive at the receiver, is limited by the number
of different codes. With a spread factor *N* and *N _{u}* users,
perfectly orthogonal codes can chosen if

(For Walsh-Hadamard codesN/_{u}N) - 1 R_{max}^{2}= ------------N- 1_{u}

In *a*synchronous CDMA, codes arrive in a time-shifted manner, and the crosscorrelation values
typically are much larger.
Asynchronous CDMA occurs in the uplink of cellular systems.

- ML code sequences can simply be generated by a shift register with feedback.
- ML linear feedback shift-register sequences have very low autocorrelation values. This implies that
- ML sequences can be used in systems that need to operate in channels with large delay spreads in multipath channels, see e.g. the rake receiver.
- the synchronisation performance is good

The simplest matrix of 2 orthogonal Walsh-Hadamard sequences is

1 1 CThe code of user 1 is the first column, i.e., (1, 1), the code of user 2 is the second column, i.e., (1, -1). Clearly (1, 1) is orthogonal to (1, -1). This matrix can be extended using a recursive technique. For 2_{1}= [ ] 1 -1

C_{(n-1)}C_{(n-1)}C_{n}= [ ] C_{(n-1)}-C_{(n-1)}

- Multi-User interference
- the asynchronous multipath
interference, arising from the delayed signals from
- the other users as well as
- user himself

- D.V. Sarwate and M.B. Pursley, "Crosscorrelation properties of pseudorandom and related sequences", Proceedings of the IEEE, Vol. 68, No. 5, May 1980, pp. 593-619.
- R. Gold, "Optimal binary sequences for spread spectrum multiplexing," IEEE Trans. Information Theory, vol. IT-13, pp. 619-621, 1967.
- M.B Pursley, "Performance evaluation for phase coded spread-spectrum multiple access communication - Part I: System Analysis," IEEE Trans. Comm., COM-25 (August 1977), pp. 795-799.
- E. Geraniotis and B. Ghaffari, "Performance of binary and quaternary direct sequence spread-spectrum multiple-access systems with random signature sequences," IEEE Trans. Comm., COM-39, No. 5, pp. 713-724, May 1991.
- D.V. Sarwate et al, "Partial correlation effects in direct-sequence multiple-access communication systems," IEEE Trans. Comm., COM-32, No. 5, pp. 567-573, May 1984.
- F.D. Garber, M.B. Pursley, "Optimal phases of maximal-length sequences for asynchronous spread - spectrum multiplexing," Electron. Lett., Vol. 16, pp. 756-757, Sept. 1980.