The correct answer is: A. Must be less than or equal to 12.288 Ã 103 bits per second
The processing gain is defined as the ratio of the bandwidth of the transmitted signal to the bandwidth of the received signal. In a Direct Sequence CDMA system, the bandwidth of the transmitted signal is equal to the chip rate. The bandwidth of the received signal is equal to the data rate. Therefore, the processing gain is given by:
$$G = \frac{B_t}{B_r} = \frac{f_c}{f_d}$$
where $f_c$ is the chip rate and $f_d$ is the data rate.
The processing gain is desired to be at least 100. Therefore, we have:
$$G \geq 100 = \frac{f_c}{f_d}$$
$$f_d \leq \frac{f_c}{100} = \frac{1.2288 \times 10^6}{100} = 1.2288 \times 10^3$$
Therefore, the data rate must be less than or equal to 12.288 kilobits per second.
Option B is incorrect because the data rate must be less than or equal to 12.288 kilobits per second, not greater than.
Option C is incorrect because the data rate must be less than or equal to 12.288 kilobits per second, not exactly equal to 12.288 kilobits per second.
Option D is incorrect because the data rate must be less than or equal to 12.288 kilobits per second, not any value less than 122.88 kilobits per second.