If the instantaneous gain realization supports the rate, i.e., g n ≥ ĝ n, m, the transmitted data is successfully decoded; otherwise outage occurs.
In this paper, the "incomplete information" particularly refers to a situation where each only knows its own channel gain realization, but does not know the channel gains of other transmitters.
If the instantaneous gain realization is within the region g ~ n, m ≤ g n < ĝ n, m + 1 (the outage region in Figure1a), the data is lost, and the transmitted information has no contribution on the system throughput.
If the current gain realization of the winner user n is within the region g ~ n, m ≤ g n < ĝ n, m + 1, the data transmitted at rate log ( 1 + ĝ n, m + 1 T n, m + 1 ) is lost, and the power Tn,m+1 is wasted.
Here, (a) is based on the fact that as the n th user gain realization is in the region Sn,m, the optimal considered gain ĝ n, m must be within this region as well, i.e., ĝ n, m ∈ S n, m.
Assuming a fast-fading model, i.e., the channels take new values in each retransmission round, the received SINR of the i-th user in round n is u ( n ) = P g i ( n ) 1 + P ∑ j = 1 ≠ i N g j ( n ) where g i (n) represents the gain realization of the channel between the i-th user and its corresponding BS at round n.
Cell-based simulation using 100 random channel gain realizations.
Intuitively, using optimal power allocation the power is not wasted on weak channel realization and the saved power is spent on strong gain realizations.
Intuitively, using long-term power allocation, the power is not wasted on weak channel realizations, and the saved power is spent on strong gain realizations.
That is, with fixed-length coding, on which we focus, the throughput degenerates to the average rate defined as expectation on achievable rates for different gain realizations.
In a -user MAC, to have "complete information" means that, at each time, the channel gain realizations are known at all the transmitters, denoted by.
