Ergodic Capacity (Uniform Fading)

Problem

Return the ergodic capacity in bits of a channel whose SNR is uniform on [a, b]:

C = (f(b) - f(a)) / ((b - a) * ln(2)), f(x) = (1 + x) * ln(1 + x) - x

Assume b > a >= 0.

Hint

Averaging log2(1 + gamma) over the fading distribution gives the ergodic capacity.

case 1

in: [0,1]

expected: 0.5573049591110365

case 2

in: [0,2]

expected: 0.934748710192771

case 3

in: [1,2]

expected: 1.3121924612745053

case 4

in: [0,4]

expected: 1.4597150777202395

Starter codePython

import math
def ergodic_capacity_uniform(a, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor