SIMO Rayleigh Fading Channel Simulation with MRC

EIE4003/MCE6004 Wireless Communications — Assignment #4

Simulation of QPSK and 16QAM modulation over a SIMO Rayleigh fading channel using Maximal Ratio Combining (MRC).

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Project Structure

SIMO_MRC/
├── main_project.m          ← Entry point — run this file only
├── README.md
├── .gitignore
├── results/                ← Saved .fig files (auto-created on first run)
└── +WirelessSim/           ← MATLAB package: all utility functions
    ├── generateQPSKSymbols.m
    ├── generate16QAMSymbols.m
    ├── applyAWGN.m
    ├── applyRayleighFading.m
    ├── simoMRC.m
    ├── qpskDemodulate.m
    ├── qam16Demodulate.m
    ├── calculateBER.m
    └── plotConstellations.m

+WirelessSim/ is a MATLAB package (the + prefix is a MATLAB convention). All utility functions are namespaced under WirelessSim.*, preventing conflicts with MATLAB built-ins and making call sites explicitly traceable to this module.

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How to Run

1. Open MATLAB
2. cd into the SIMO_MRC/ folder
3. Run main_project.m

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System Model

Transmitter ──► SIMO Rayleigh Channel ──► MRC Combiner ──► Demodulator
  (1 TX)          (Nr RX antennas)         (equalize)     (QPSK/16QAM)

Each receive antenna observes:

$$y_r = h_r \cdot x + n_r, \quad r = 1, 2, \ldots, N_r$$

where $h_r \sim \mathcal{CN}(0, 1)$ is the Rayleigh fading coefficient and $n_r$ is AWGN.

MRC combining:

$$\hat{x} = \frac{\sum_{r=1}^{N_r} h_r^* \cdot y_r}{\sum_{r=1}^{N_r} |h_r|^2}$$

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Parameters

Parameter	Value
SNR range	−5 dB to 25 dB (25 points)
Bits per SNR point	200,000
Antenna configs	1×1, 1×2, 1×4
Modulations	QPSK (2 bits/symbol), 16QAM (4 bits/symbol)
Channel	i.i.d. Rayleigh fading

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Output Files

Running main_project.m will automatically generate a results/ folder containing:

File	Description
BER_QPSK.fig	QPSK BER curves for 1×1, 1×2, 1×4 MRC
BER_16QAM.fig	16QAM BER curves for 1×1, 1×2, 1×4 MRC
BER_Comparison.fig	QPSK vs 16QAM comparison (1×4 MRC)
Constellation_QPSK.fig	QPSK constellation diagrams at SNR = 5/20 dB
Constellation_16QAM.fig	16QAM constellation diagrams at SNR = 5/20 dB

Key Results

• MRC diversity gain: each doubling of receive antennas significantly reduces BER
• QPSK outperforms 16QAM at the same SNR (lower spectral efficiency, higher robustness)
• With 1×4 MRC, BER performance approaches the AWGN theoretical bound at high SNR