8.5.2 Spreading And Processing Gain

In direct-sequence CDMA, each information bit is multiplied by a higher-rate binary sequence known as the spreading code. If the information bit duration is T_b and the chip duration is T_c, then each information bit is represented by:

N = \frac{T_{b}}{T_{c}}

(8.8)

chips. The chip rate is therefore R_c=1/T_c and the original bit rate is R_b=1/T_b.

Because the signal transitions at the chip rate rather than the bit rate, its spectrum expands approximately in proportion to R_c. The spread bandwidth W is therefore on the order of the chip rate. The processing gain may be expressed as:

G_{p} = \frac{R_{c}}{R_{b}} = \frac{T_{b}}{T_{c}}

(8.9)

Processing gain has two complementary interpretations. In the transmitter, it represents bandwidth expansion relative to the information rate. In the receiver, it represents the factor by which interference power is reduced after correlation with the desired spreading sequence.

When the received composite signal is multiplied by the locally generated spreading code and integrated over one bit interval, the desired signal adds coherently, while uncorrelated interference averages toward zero. The improvement in signal-to-interference ratio after de-spreading is approximately equal to the processing gain, assuming ideal statistical independence between users’ codes.

This relationship illustrates the fundamental trade-off of CDMA: increasing processing gain improves interference tolerance but requires a proportionally larger bandwidth. CDMA therefore converts bandwidth into interference resilience.

Unlike FDMA, where spectral efficiency is determined by channel spacing and guard bands, and unlike TDMA, where efficiency is influenced by guard times and burst overhead, CDMA efficiency depends on how many users can be supported within a given interference level for a specified processing gain.