Note that the condition (1.4), which is stated as ρ * > max { ( δ σ B 1 * ) δ, ( δ σ B 1 * ) 1 σ }. is crucial to guarantee that R > 1 > r0, and in the proof of Theorem 1.3 we require R > 1 > r0 because the exponents in inequalities of (A3) is different.
The random access NUM is stated as follows[1, 9] ( P 1 ) : max.
If only the "[max]" is stated, then the "[min]" is assumed to be the lowest number in that particular parameter.
If only the "[min]" is stated, then the "[max]" is assumed to be the highest number in that particular parameter.
Using (7), (10) and the power constraint T ̄ ≤ T, the power-limited average rate maximization problem can be stated as max g ̃ i, ĝ i, T i 2 ∑ i = 2 N P i R i + ∑ i = 1 N Q i R i subject to 2 ∑ i = 2 N P ′ i T i + ∑ i = 1 N Q ′ i T i ≤ T (13).
In this perspective, for a power constraint T, the power-limited throughput optimization problem can be stated as R ̄ max ( 1, …, N ) = max ∀ g ~ n, m, ĝ n, m, T n, m ∑ n = 1 N ∑ m = 1 M n φ n, m β n, m log 1 + ĝ n, m T n, m s.t.
Then, the optimization problem can be stated as solving max t j j = 1, …, m Φ. (2).
The dual function g can now be stated as g = max L ( μ k, λ ) s.t.
Unicolumn statistics are stated in terms of min., max., average, std.
We also define: T max is the maximum number of states that any state in the model is connected to, also called the model's connectivity.
