Multiple-Input
Multiple-Output

Master the technology that revolutionized wireless communications. Explore spatial multiplexing, diversity, and beamforming through interactive simulations.

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Fundamental Concepts

Spatial Multiplexing

Transmitting independent data streams simultaneously over multiple antennas to increase spectral efficiency. The key to high data rates in 4G/5G.

Diversity Gain

Combating multipath fading by sending redundant signals over different paths. Improves link reliability and reduces bit error rate (BER).

Beamforming

Directing signal energy towards specific users using phase shifts. Increases SNR and allows for spatial division multiple access (SDMA).

Interactive MIMO Channel Visualizer

Adjust parameters to see how antennas and SNR affect channel capacity.

System Parameters

2
2
20 dB
Channel Capacity
0.00 bits/s/Hz
C = log₂(det(I + SNR/Nt · H·Hᴴ))

Channel Matrix (H)

Visualization of the Nr × Nt channel matrix coefficients.

Capacity vs. SNR Comparison

The Mathematics of MIMO

MIMO systems are described by the linear equation:

y = Hx + n
  • y Received signal vector (Nr × 1)
  • H Channel matrix containing complex gains (Nr × Nt)
  • x Transmitted signal vector (Nt × 1)
  • n Additive White Gaussian Noise (AWGN)

Ergodic Capacity Formula

C = E[log₂ det(INr + SNR/Nt · HHH)]

Where INr is the identity matrix, and HH is the Hermitian (conjugate transpose) of H. The expectation E[·] is taken over the random channel matrix H.

Key Insight

At high SNR, capacity grows linearly with min(Nt, Nr), effectively multiplying the data rate by the number of antennas.

MIMO in Modern Standards

How MIMO is implemented in current wireless technologies.

802.11n
Wi-Fi 4

Introduced MIMO to Wi-Fi. Supports up to 4 spatial streams. Data rates up to 600 Mbps.

LTE
4G Mobile

Downlink supports up to 8x8 MIMO. Uplink typically uses MU-MIMO to save battery.

802.11ac
Wi-Fi 5

Expanded to 8 spatial streams. Introduced Multi-User MIMO (MU-MIMO) for downlink.

5G NR
New Radio

Massive MIMO (64+ antennas at base station) and mmWave beamforming are core technologies.