LTE 2-User MIMO (Uplink) – Step-by-Step Example
This example shows how two mobile users transmit simultaneously and how the base station separates their signals using linear algebra.
1. Transmission
x = [ x1
x2 ]
- x1: Signal from User 1
- x2: Signal from User 2
2. Channel Matrix
H = [ 1 0.5
0.3 1 ]
Signals from both users mix across both receive antennas.
3. Received Signal
y = Hx
y1 = x1 + 0.5x2 y2 = 0.3x1 + x2
The base station receives only mixed signals — no clean separation exists.
4. Detection Using Zero Forcing (ZF)
x̂ = H⁻¹ y
Inverse of H
det(H) = 1 - (0.5 × 0.3) = 0.85
H⁻¹ = (1 / 0.85) × [ 1 -0.5
-0.3 1 ]
H⁻¹ = [ 1.176 -0.588
-0.353 1.176 ]
5. Recover Signals
x̂1 = 1.176y1 - 0.588y2 x̂2 = -0.353y1 + 1.176y2
6. Substitution
For x̂1:
x̂1 = 1.176(x1 + 0.5x2) - 0.588(0.3x1 + x2)
= x1
For x̂2:
x̂2 = -0.353(x1 + 0.5x2) + 1.176(0.3x1 + x2)
= x2
Final Result:
x̂1 = x1 x̂2 = x2
Both user signals are perfectly recovered using matrix inversion.
7. Summary
- Signals are fully mixed in the air
- No signal is discarded
- Receiver uses math (matrix inversion) to separate them
Old LTE MIMO works as:
- Mix signals → y = Hx
- Invert channel → x = H⁻¹y
- Recover all user data
This is a pure linear algebra problem solved at the base station.