Consider an FDMA system with K orthogonal sub channels. Within each sub channel the transmission…

Consider an FDMA system with K orthogonal sub channels. Within each sub channel the transmission follows a slotted ALOHA scheme. For the input process consider the infinite population case with offered normalized traffic G.

a) Find the normalized throughput of this system when the K sub channels are selected uniformly at random by any input packet.

b) Compare the normalized throughput S(K, G) with respect to the throughput of a single channel ALOHA system, S(1, G), find the throughput gain in terms of the ratio η(K, G) = S(K, G)/S(1, G) and find the minimum number of sub channels K to use so that η > 1, for any G. Finally, determine the maximum achievable gain, η, as a function of G.