MIMO Capacity

Problem

Compute the capacity in bits per channel use of a 2x2 MIMO channel: C = log2 det(I + (snr / n_t) H H^T) with n_t = 2 transmit antennas. Build M = H H^T, set g = snr / 2, form the 2x2 matrix with entries (1 + g * M00), (g * M01), (g * M01), (1 + g * M11), and return the base-2 log of its determinant.

Hint

An identity channel diagonalizes the determinant into two independent paths.

Test cases

case 1

in: [[[1,0],[0,1]],2]

expected: 2

case 2

in: [[[1,0],[0,1]],0]

expected: 0

case 3

in: [[[1,0.5],[0.5,1]],10]

expected: 4.7846348455575205

case 4

in: [[[1,1],[1,1]],4]

expected: 3.169925001442312

Starter codePython

import math
def mimo_capacity(h, snr):
    # Your code here
    pass

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