⚡ electrical engineering

MIMO-AFDM Outperforms MIMO-OFDM in the Face of Hardware Impairments

This paper demonstrates that MIMO-AFDM systems outperform conventional MIMO-OFDM in the presence of hardware impairments by maintaining full diversity order and exhibiting superior resilience to both multiplicative and additive distortions, attributed to their inherent chirp signal characteristics and the spreading effect of the discrete affine Fourier transform.

Original authors: Zeping Sui, Zilong Liu, Leila Musavian, Yong Liang Guan, Lie-Liang Yang, Lajos Hanzo

Published 2026-05-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Zeping Sui, Zilong Liu, Leila Musavian, Yong Liang Guan, Lie-Liang Yang, Lajos Hanzo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Race Against a Noisy World

Imagine you are trying to send a secret message to a friend using a series of flashlights in a crowded, windy stadium. This is what modern wireless networks (like 5G and future 6G) do: they send data using radio waves.

The paper compares two different ways of organizing these "flashlights" (signals):

MIMO-OFDM: The current standard. It's like arranging the flashlights in neat, rigid rows. It works great when the air is still, but if the wind blows hard (high speed) or the flashlights are cheap and flicker (hardware flaws), the rows get messy, and the message gets lost.
MIMO-AFDM: The new challenger. It uses "chirp" signals, which are like flashlights that sweep their brightness up and down in a specific pattern. The paper argues that this sweeping pattern is much tougher against wind and bad equipment.

The Problem: "Hardware Impairments" (The Flawed Equipment)

In the real world, our phones and cell towers aren't perfect. The paper focuses on the "flaws" in the hardware that mess up the signal. Think of these flaws as different types of noise in a crowded room:

Phase Noise & Frequency Offsets (The Jittery Clocks): The clocks inside the transmitter and receiver aren't perfectly synced. It's like two people trying to dance to music, but one is slightly out of step. This causes the signal to wobble.
Low-Resolution DACs (The Pixelated Camera): The device converting digital data to radio waves has low quality. It's like trying to draw a smooth curve with a blocky, pixelated crayon. This adds "grain" or static to the picture.
Nonlinear Power Amplifiers (The Overheating Speaker): When the signal gets too loud, the amplifier distorts it, like a speaker that cracks when you turn the volume to max.
IQ Imbalance & DC Offset (The Leaky Pipe): The signal leaks or has a constant "hum" that shouldn't be there, drowning out the actual message.

The Solution: Why AFDM Wins

The researchers tested both systems (OFDM and AFDM) under these "broken" conditions. Here is what they found, explained through analogies:

1. The "Chirp" Superpower
OFDM signals are like straight arrows. If the wind (Doppler shift from high speed) or the shaky hands (hardware flaws) push them, they miss the target.
AFDM signals are like boomerangs or sweeping spotlights. Because they sweep across the frequency spectrum, if the wind pushes them, they don't miss; they just land in a slightly different spot that the receiver can still catch.

The Result: AFDM is much more resilient to "multiplicative" distortions (like the jittery clocks and frequency offsets). Even with bad hardware, the signal stays strong.

2. The "Spreading" Effect
OFDM keeps its data in tight, separate lanes. If one lane gets blocked by noise (from a bad amplifier), that whole piece of data is lost.
AFDM spreads its data out over the entire road (time and frequency). If a pothole (noise) hits one part of the road, the rest of the message is still safe.

The Result: When the hardware adds "static" (additive noise like from low-quality converters), AFDM can average it out and recover the message much better than OFDM.

3. The "Full Diversity" Guarantee
In wireless terms, "diversity" means having multiple backup paths for your message.

The Finding: Even with all the broken hardware, AFDM still manages to use all its available backup paths. It doesn't lose its ability to recover from errors. OFDM, on the other hand, often loses this ability when the hardware is imperfect, leading to a "floor" where the error rate stops improving no matter how much power you add.

The Proof: What the Math and Simulations Showed

The authors did two main things to prove this:

The Math: They wrote complex equations to predict exactly how often the system would make a mistake (Bit Error Rate). They found that for small systems, they could calculate a "worst-case" limit, and for big systems, they could predict the average performance.
The Simulation: They ran computer tests mimicking high-speed trains and bad hardware.
- Result A: When the hardware was perfect, AFDM was already better.
- Result B: When the hardware was "broken" (simulating real life), OFDM's performance crashed hard. AFDM's performance dipped slightly but stayed strong.
- Result C: AFDM handled high speeds (like a train moving at 540 km/h) much better than OFDM.

The Bottom Line

The paper concludes that MIMO-AFDM is a tougher, more reliable way to send data than the current standard (OFDM), especially when:

You are moving very fast (high Doppler).
The hardware isn't perfect (cheap or aging equipment).

It achieves this because its unique "chirp" shape and "spreading" nature act like a shock absorber, smoothing out the bumps caused by bad hardware and high speeds. The researchers suggest that future networks should consider switching to this technology to keep our connections stable, even when the equipment isn't perfect.

Technical Summary: MIMO-AFDM Outperforms MIMO-OFDM in the Face of Hardware Impairments

1. Problem Statement

Next-generation wireless networks targeting high-mobility environments (e.g., high-speed trains, drones, low-earth-orbit satellites) face severe inter-carrier interference (ICI) and inter-symbol interference (ISI) due to high Doppler shifts. While Orthogonal Frequency Division Multiplexing (OFDM) is the current standard, it suffers from orthogonality erosion under these conditions. Although Affine Frequency Division Multiplexing (AFDM) has emerged as a promising alternative due to its chirp-based signaling and Discrete Affine Fourier Transform (DAFT) domain, existing literature primarily assumes ideal hardware or perfect Channel State Information (CSI).

In practical systems, severe performance degradation occurs due to non-ideal hardware, including:

Multiplicative Impairments: Oscillator Phase Noise (PN) and Carrier Frequency Offset (CFO).
Additive Impairments: Quantization distortions from low-resolution Digital-to-Analog Converters (DACs), In-phase and Quadrature Imbalance (IQI), Nonlinear Power Amplifier (NPA) distortions, and Direct Current Offset (DCO).

The core problem addressed is the lack of a comprehensive performance analysis for Multiple-Input Multiple-Output (MIMO)-AFDM systems under realistic hardware impairments (HWIs) and imperfect CSI, specifically comparing its resilience against conventional MIMO-OFDM.

2. Methodology

The authors develop a rigorous analytical framework to model and evaluate MIMO-AFDM systems under various HWIs.

System Modeling: The study derives the end-to-end input-output relationship for MIMO-AFDM in the DAFT domain, incorporating both multiplicative (PN, CFO) and additive (DAC quantization, IQI, NPA, DCO) distortions. The model accounts for both co-located (CLO) and separate (SLO) local oscillators.
Signal Characterization: The derived model identifies specific interference terms introduced by HWIs, including mirror interference (from IQI), DC interference (from DCO and PN/CFO), and nonlinear-distortion interference (from NPA and DACs).
Performance Analysis:
- Small-Scale Systems: A tight Bit Error Rate (BER) upper bound is derived for Maximum Likelihood (ML) detectors. The analysis focuses on Pairwise Error Probability (PEP) to determine diversity order.
- Large-Scale Systems: A closed-form BER approximation is presented for Linear Minimum Mean Squared Error (LMMSE) detectors, incorporating channel estimation errors.
Diversity Analysis: The authors mathematically prove that the diversity order of the system is determined by the rank of the codeword distance matrix and the channel covariance, specifically examining whether HWIs degrade this order.
Simulation: Extensive Monte-Carlo simulations compare MIMO-AFDM against MIMO-OFDM under various scenarios, including different velocities, CFO values, phase noise variances, DAC resolutions, and PA clipping levels.

3. Key Contributions

The paper makes the following specific contributions to the literature:

Comprehensive HWI Modeling: For the first time in AFDM literature, the authors derive the DAFT-domain input-output relationship for MIMO-AFDM systems considering a full suite of HWIs (PN, CFO, low-resolution DACs, IQI, NPA, and DCO). This includes modeling the resulting mirror, DC, and nonlinear-distortion interference terms.
Diversity Order Preservation: The analysis demonstrates that despite the presence of HWIs, the MIMO-AFDM system employing an ML detector retains its full diversity order. This is attributed to the fact that multiplicative HWI matrices (PN and CFO) are diagonal, preserving the rank properties of the channel matrix.
Analytical Bounds:
- A closed-form BER upper bound for ML detectors in small-scale systems is derived, which is shown to be tight at moderate-to-high Signal-to-Noise Ratios (SNRs).
- A closed-form BER approximation for LMMSE detectors in large-scale systems is presented, accounting for imperfect CSI.
Comparative Resilience: The study provides quantitative evidence that MIMO-AFDM is significantly more resilient to HWIs than MIMO-OFDM. Specifically, AFDM maintains performance under CFO and PN where OFDM suffers from error floors, and it outperforms OFDM under additive HWIs due to its inherent ICI resilience and time-frequency spreading.

4. Key Results

Simulation results and theoretical analysis yield the following observations:

Resilience to Multiplicative Impairments: MIMO-AFDM maintains performance nearly identical to the ideal hardware case under CFO and PN. In contrast, MIMO-OFDM exhibits significant SNR loss and error floors (e.g., 8 dB loss at BER $10^{-4}$ for normalized CFO $\phi_{CFO}=0.08$ ).
Resilience to Additive Impairments:
- Low-Resolution DACs: AFDM shows superior performance compared to OFDM. For 5-bit DACs, AFDM suffers only ~1 dB SNR loss compared to ideal hardware, whereas OFDM suffers ~8 dB.
- IQI and NPA: AFDM consistently achieves lower BER than OFDM under identical IQI and PA nonlinearity settings. The chirp structure and DAFT spreading effect allow AFDM to average out uncorrelated quantization noise and mitigate ICI caused by nonlinear distortions.
Diversity Order: Theoretical analysis confirms that the diversity order of hardware-impaired MIMO-AFDM remains $P \times J$ (where $P$ is the number of paths and $J$ is the number of receive antennas), identical to the ideal case.
Velocity Robustness: AFDM outperforms OFDM across all velocity ranges, including static scenarios, by extracting multipath diversity from delay spread even without Doppler spread.
Channel Matrix Structure: Visualizations of the effective channel matrices show that AFDM preserves a sparse structure with non-overlapping non-zero elements (diagonal and sub-diagonal lines), enabling full diversity. In contrast, OFDM matrices under HWIs show overlapping elements, preventing full diversity exploitation.

5. Significance and Claims

The paper claims that MIMO-AFDM is a robust waveform candidate for next-generation high-mobility networks, particularly in environments where hardware imperfections are unavoidable.

Unique Advantage: The primary significance lies in the finding that AFDM's "full diversity order" is unaffected by hardware impairments. This is a unique advantage over OFDM, where HWIs often degrade diversity gains and cause error floors.
Backward Compatibility: The authors emphasize that AFDM can be implemented with minimal modifications to existing OFDM architectures, making it a practical, backward-compatible solution.
Design Guidance: The results suggest that system designers can rely on AFDM to achieve maximum diversity gains even with lower-cost hardware (e.g., lower-resolution DACs or less stable oscillators), provided the chirp parameters ( $c_1, c_2$ ) are appropriately tuned.
Limitations and Future Work: The authors modestly note that while AFDM is resilient to multiplicative distortions, it remains sensitive to additive HWIs (though less so than OFDM). They identify future research directions including HWI mitigation techniques, synchronization, and the impact of fractional delay and time offset (TO) estimation errors on AFDM performance.