4×4 MIMO in LTE (Signal Processing Perspective)

This explains how a 4×4 MIMO system works in LTE, extending the 2×2 case to a more realistic scenario.

1. System Setup

• 4 transmitted signals (streams/users)
• 4 receive antennas at base station

2. Signal Model

y = Hx + n

x = [ x1
      x2
      x3
      x4 ]

y = [ y1
      y2
      y3
      y4 ]

3. Channel Matrix

H = [ h11 h12 h13 h14
      h21 h22 h23 h24
      h31 h32 h33 h34
      h41 h42 h43 h44 ]

Each receive antenna gets a mixture of all transmitted signals.

4. Received Signal Expansion

y1 = h11x1 + h12x2 + h13x3 + h14x4
y2 = h21x1 + h22x2 + h23x3 + h24x4
y3 = h31x1 + h32x2 + h33x3 + h34x4
y4 = h41x1 + h42x2 + h43x3 + h44x4

All received signals are mixtures — no antenna gets a clean signal.

5. Detection Techniques

(A) Zero Forcing (ZF)

x̂ = H⁻¹ y

• Removes interference
• Sensitive to noise

(B) MMSE (Used in LTE)

x̂ = (HᴴH + N₀I)⁻¹ Hᴴ y

• Balances noise and interference
• More stable than ZF

(C) Successive Interference Cancellation (SIC)

1. Detect strongest signal (e.g., x1)
2. Subtract its effect
3. Detect next signal
4. Repeat

Also known as V-BLAST detection

6. Challenges in 4×4 MIMO

• Noise amplification during inversion
• Channel correlation (antennas not independent)
• High computational complexity

7. Practical LTE Usage

• Often used for a single user (SU-MIMO)
• Multiple streams (layers) for higher data rate
• Limited multi-user MIMO

8. Summary

• Signals are fully mixed in the air
• No signal is discarded
• Receiver separates signals using advanced algorithms

• Mix signals → y = Hx
• Apply detection → x = detector(H, y)
• Recover all transmitted signals

4×4 MIMO follows the same principle as 2×2, but requires more advanced processing due to higher complexity.