OFDM Performance Analysis
Measuring OFDM Performance
This section brings everything together: simulate a complete OFDM system over frequency-selective channels and measure BER, throughput, and spectral efficiency.
Definition: Effective SNR for OFDM
Effective SNR for OFDM
The effective SNR maps the per-subcarrier SNR vector to a single number predicting system performance. The exponential effective SNR mapping (EESM) is:
where is a modulation-dependent parameter.
Theorem: OFDM BER as Average of Subcarrier BERs
With perfect channel knowledge and ZF equalization, the average BER of OFDM with -QAM is:
Each subcarrier contributes its own BER based on its effective SNR.
OFDM decomposes the problem into independent AWGN channels, each with its own SNR determined by the channel response at that frequency.
Example: OFDM BER Simulation Over Multipath
Simulate OFDM BER with 16-QAM over a 5-tap channel and compare ZF vs MMSE equalization.
Implementation
# See code supplement ch22/python/ofdm_system.py
OFDM BER Over Multipath Channel
Simulate OFDM BER with different modulation orders and channel models.
Parameters
OFDM Constellation vs SNR
Watch the equalized constellation improve as SNR increases.
Parameters
OFDM Parameters in Wireless Standards
| Parameter | LTE (20 MHz) | 5G NR (100 MHz) | Wi-Fi 6 (160 MHz) |
|---|---|---|---|
| FFT Size | 2048 | 4096 | 2048 |
| Subcarrier Spacing | 15 kHz | 30 kHz | 78.125 kHz |
| CP Length | 144/160 samples | 288 samples | 0.8/1.6 us |
| Data Subcarriers | 1200 | 3276 | 1960 |
| Modulation | Up to 256-QAM | Up to 256-QAM | Up to 1024-QAM |
Common Mistake: Channel Longer Than CP
Mistake:
Simulating with a channel whose delay spread exceeds the CP length without realizing the BER floor it creates.
Correction:
Always check: assert len(h) - 1 <= N_cp. If the channel is too long,
either increase the CP or accept the BER floor and model the ISI.
Historical Note: OFDM in Wi-Fi
1999IEEE 802.11a (1999) was the first mass-market wireless system using OFDM, with 64 subcarriers at 20 MHz bandwidth. Its success demonstrated that OFDM could be implemented cost-effectively with commodity DSPs, paving the way for LTE and 5G adoption.