Consider an FH CDMA system that uses FSK modulation and the same spreading and information bandwidth as the DS CDMA system in Problem 14.3. Thus, there are G = 100 frequency slots in the system, each of bandwidth 100 kHz. The hopping codes are random and uniformly distributed, so the probability that a given user occupies a given frequency slot on any hop is .01. As in Problem 14.3, noise is essentially negligible, so the probability of error on a particular hop is zero if only one user occupies that hop. Also assume perfect power control, so the received power from all users is the same.
(a) Find an expression for the probability of bit error when m users occupy the same frequency slot.
(b) Assume there is a total of K users in the system at any time. What is the probability that, on any hop, there is more than one user occupying the same frequency?
(c) Find an expression for the average probability of bit error as a function of K, the total number of users in the system.
Problem 14.3
Consider a DS CDMA system occupying 10 MHz of spectrum. Assume an inter ferencelimited system with a spreading gain of G = 100 and code cross-correlation of 1/G.
(a) For the MAC, find a formula for the SIR of the received signal as a function of G and the number of users K. Assume that all users transmit at the same power and that there is perfect power control, so all users have the same received power.
(b) Based on your SIR formula in part (a), find the maximum number of users K that can be supported in the system, assuming BPSK modulation with a target BER of 10-3. In your BER calculation you can treat interference as AWGN. How does this compare with the maximum number of users K that an FDMA system with the same total bandwidth and information signal bandwidth could support?
(c) Modify your SIR formula in part (a) to include the effect of voice activity, defined as the percentage of time that users are talking, so interference is multiplied by this percentage. Also find the voice activity factor such that the CDMA system accommodates the same number of users as an FDMA system. Is this a reasonable value for voice activity?