Laboratory Objectives
1. Understand Spatial Multiplexing
To visualize how multiple data streams can be transmitted simultaneously over the same frequency band using multiple antennas.
2. Analyze Channel Capacity
To observe the relationship between Signal-to-Noise Ratio (SNR), number of antennas, and the theoretical Shannon Capacity limit.
3. Simulate Rayleigh Fading
To understand the impact of multipath fading on signal constellation diagrams and bit error rates.
4. Compare SISO vs MIMO
To quantitatively compare the performance of Single-Input Single-Output systems against 2x2 and 4x4 MIMO configurations.
Theoretical Background
The MIMO System Model
MIMO technology uses multiple antennas at both the transmitter (Tx) and receiver (Rx) to improve communication performance. The fundamental equation governing a MIMO system is:
- y: Received signal vector (Rx Antennas × 1)
- H: Channel Matrix (Rx × Tx) representing fading coefficients.
- x: Transmitted signal vector (Tx Antennas × 1)
- n: Additive White Gaussian Noise (AWGN)
Shannon Capacity in MIMO
Unlike SISO systems, MIMO capacity grows linearly with the minimum number of antennas (min(Nt, Nr)) at high SNR. The ergodic capacity for a random MIMO channel is given by:
Where I is the identity matrix and HH is the Hermitian transpose.
Interactive Simulation
Configuration
Live Metrics
Constellation Diagram (Rx)
Capacity vs SNR
Laboratory Procedure
Step 1: Baseline SISO Analysis
Set the antenna configuration to 1x1 (SISO). Select QPSK modulation. Vary the SNR from 0dB to 40dB.
- Observe the constellation diagram. How does the noise affect the points?
- Note the Capacity value. Does it match the Shannon limit for SISO (log₂(1+SNR))?
Step 2: Introduce Spatial Multiplexing (2x2)
Change configuration to 2x2 MIMO. Keep QPSK.
- Observe the visualizer. Two distinct data streams should be visible.
- Compare the Capacity value to the SISO case. It should roughly double at high SNR.
- Examine the Constellation Diagram. You may see two overlapping QPSK constellations representing the two streams.
Step 3: Impact of Channel Correlation
In a real lab, we would change antenna spacing. Here, observe the Condition Number.
- A low condition number (close to 1) means the channel matrix is well-conditioned (good for MIMO).
- A high condition number means the streams are interfering significantly (bad for MIMO).
- Run the simulation multiple times. The channel matrix H is random (Rayleigh fading). Notice how capacity fluctuates even at constant SNR.
Step 4: Higher Order MIMO (4x4)
Switch to 4x4 MIMO.
- Observe the massive increase in throughput (Capacity).
- Switch modulation to 64-QAM. Observe the density of the constellation diagram.
Report Guidelines
Prepare a comprehensive report documenting your findings. The report should include the following sections:
Required Sections
- Aim: State the objectives of the experiment.
- Theory: Briefly explain the MIMO system model and capacity formula.
- Simulation Setup: List the parameters used (Antennas, Modulation, SNR range).
- Results: Include screenshots of the Constellation Diagram and Capacity graphs for 1x1, 2x2, and 4x4 at a fixed SNR (e.g., 20dB).
- Analysis: Discuss the capacity scaling. Why does 4x4 not always give 4x the capacity of SISO?
Key Questions to Answer
- What is the significance of the Channel Matrix H being full rank?
- How does increasing SNR affect the Bit Error Rate (BER) in your observations?
- If the Condition Number is very high (e.g., > 20), what does it imply about the radio environment?
- Calculate the theoretical capacity for a 2x2 system at 10dB SNR assuming an identity channel matrix.