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Technical Supplement Report on Full-Duplex FBMC/QAM MIMO Systems: Transceiver Design and Optimization

This technical report designs and analyzes full-duplex FBMC/QAM MIMO systems by characterizing their end-to-end effective channels, comparing them with CP-OFDM and FBMC/OQAM through the Balian-Low theorem and various prototype filters, and proposing an online stochastic optimization framework that demonstrates superior spectral efficiency and BER performance under residual carrier frequency offset.

Original authors: Sudhakar Rai, Prem Singh, Ekant Sharma, Aditya K. Jagannatham, Lajos Hanzo

Published 2026-06-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sudhakar Rai, Prem Singh, Ekant Sharma, Aditya K. Jagannatham, 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

Imagine a busy highway where cars (data) are constantly trying to drive in both directions at the same time. In the world of wireless communication, this is called Full-Duplex: sending and receiving data simultaneously on the same frequency. The challenge is that your own transmission is so loud it drowns out the quiet voice of the person you are trying to hear. This is like trying to listen to a friend whisper while you are shouting into a megaphone right next to your ear.

This technical supplement is a "behind-the-scenes" guide to a new way of organizing traffic on this highway to make it faster and clearer. Here is the breakdown of what the paper does, using simple analogies.

1. The Problem: The "Traffic Jam" of Signals

In traditional systems (like OFDM, which your Wi-Fi uses), data is sent in neat, rectangular blocks. To keep the blocks from crashing into each other, engineers have to leave empty space (called a "Cyclic Prefix") between them. This is like putting a buffer zone between cars on a highway; it keeps them safe, but it wastes road space, reducing the total number of cars you can fit.

The authors are using a newer, more efficient system called FBMC/QAM. Think of this as a system where the cars are shaped like smooth, rounded pebbles. They can be packed much tighter together without crashing, meaning you can fit more data in the same amount of space. However, because they are packed so tightly, they are prone to "intrinsic interference"—a bit of noise caused by the pebbles rubbing against each other.

2. The Solution: The "Dual-Filter" Strategy

To manage this tight packing, the authors use a clever trick involving filters. Imagine the highway is divided into two lanes: an "Even" lane and an "Odd" lane.

The Even Lane uses one specific type of smooth pebble (a filter).
The Odd Lane uses a slightly different, "sibling" pebble.

By using two different but complementary shapes for alternating lanes, the system cancels out most of the rubbing noise (interference) that would happen if everyone used the same shape. This is the core of their design: Dual-Filter FBMC/QAM.

3. The "Self-Interference" Challenge

Since the system sends and receives at the same time, the "shouting" (transmitting) drowns out the "whispering" (receiving). The paper analyzes how much of the signal is actually the message you want versus how much is just the echo of your own voice or noise from other cars (interference).

They ran simulations (like a traffic simulation game) to see what happens when they try to cancel out their own shouting. They found that:

If they use a standard "Maximal Ratio Combining" strategy (trying to boost the signal as much as possible), the main problem is noise from other users.
If they use a "Zero-Forcing" strategy (trying to mathematically cancel out all noise), the main problem becomes the "rubbing" noise between the Even and Odd lanes.

4. Choosing the Right "Pebble" (The Filter)

The paper spends a lot of time deciding which specific shape of "pebble" (filter) works best. They compared three types:

PHYDYAS: The standard, well-known shape used in most research.
Type-I: A newer shape.
Type-II: Another variation.

The Surprise Finding:

For Clarity (Bit Error Rate): The Type-I filter was the winner. It made the "whisper" the clearest, with the fewest mistakes.
For Speed (Spectral Efficiency): Surprisingly, the standard PHYDYAS filter actually allowed for more total data to be sent per second, even though it wasn't the absolute clearest.

It's like choosing between a car that drives the smoothest (Type-I) and a car that can carry the most cargo (PHYDYAS). Depending on what you value most, you pick a different car. The authors stick with PHYDYAS for their main system because it offers the best overall balance for their specific setup.

5. The "Smart Traffic Controller" (Optimization)

Finally, the paper describes an algorithm (a set of rules for a computer) that decides how much power to give to each "car" (user) to maximize the total speed of the highway.

Old Way (Offline): Imagine a traffic planner who stops all traffic, looks at a map of every car that ever drove on the road, and then makes a plan. This is slow and requires a huge amount of memory.
New Way (Online Stochastic): The authors propose a "live" traffic controller. This controller doesn't need to see the whole history. It just looks at the traffic right now, makes a tiny adjustment, and then looks again in the next second. It learns as it goes.

Why this is better:
The paper proves that this "live" method is just as good as the "offline" method but is much faster and doesn't need to store massive amounts of past data. It's like a GPS that updates your route in real-time based on current traffic, rather than a map that was printed yesterday.

Summary

This paper is a technical manual for a new, high-speed wireless system. It explains:

How to pack data tighter using smooth, rounded signal shapes (FBMC) instead of blocky ones.
How to use two different "filters" (like even and odd lanes) to prevent those shapes from interfering with each other.
Which filter shape works best (finding a balance between clarity and speed).
How to manage power using a smart, real-time algorithm that learns on the fly, making the system efficient without needing a supercomputer to plan everything in advance.

The goal is simply to make full-duplex communication (sending and receiving at once) work faster and more reliably than current technology allows.

Technical Summary: Full-Duplex FBMC/QAM MIMO Systems

Problem Statement

This technical supplement supports the main paper on Full-Duplex (FD) FBMC/QAM MIMO systems. The core challenge addressed is the design and optimization of transceivers for systems that simultaneously transmit and receive on the same frequency band using Filter Bank Multi-Carrier with Quadrature Amplitude Modulation (FBMC/QAM).

The system must contend with several complex interference sources inherent to full-duplex operation and the FBMC waveform:

Self-Interference (SI): The loop interference between transmit and receive antennas at the Base Station (BS).
Intrinsic Interference: Caused by the overlapping nature of FBMC symbols and imperfect orthogonality in frequency-selective fading channels.
Inter-User Interference (IUI) and Inter-Carrier Interference (ICI): Resulting from multi-user MIMO operations and filter leakage.
CFO Impairments: Residual Carrier Frequency Offsets that degrade performance.

The objective is to maximize the Spectral Efficiency (SE) of the system under power constraints, despite the lack of closed-form expressions for the ergodic sum rate due to the complexity of the channel and interference statistics.

Methodology

1. System Modeling and Signal Processing

The paper establishes a rigorous mathematical framework for both uplink and downlink signal processing chains:

Signal Decomposition: The received signal is decomposed into desired components, intrinsic interference, ICI, ISI, and self-interference. The model utilizes Toeplitz matrices to represent multi-tap channel impulse responses and effective channel matrices in the FBMC domain.
Subcarrier Grouping: The $M$ subcarriers are grouped into $B$ groups (specifically $B=2$ for even and odd subcarriers). Distinct pulse-shaping filters are assigned to each group to mitigate intrinsic interference, a strategy motivated by the Balian-Low theorem (BLT).
Waveform Selection: The system adopts FBMC/QAM over CP-OFDM and FBMC/OQAM. While FBMC/OQAM offers excellent time-frequency localization, it sacrifices complex-field orthogonality. FBMC/QAM is chosen to maintain complex-field orthogonality and maximum symbol density (1 complex symbol per unit), accepting a trade-off in frequency localization.

2. Prototype Filter Analysis

A significant portion of the analysis focuses on the selection of the prototype filter:

PHYDYAS Filter: The system primarily utilizes the PHYDYAS filter with a dual-filter structure ( $B=2$ ). Simulations indicate that while the desired signal strength is higher for even-indexed subcarriers, interference components (ICI, ISI, and orthogonality loss) are more dominant in odd-indexed subcarriers.
Filter Comparison: The paper compares PHYDYAS against Type-I and Type-II filters (from Yun et al.).
- BER Performance: Type-I filters demonstrate superior Bit Error Rate (BER) performance compared to PHYDYAS and Type-II under residual CFO.
- Spectral Efficiency: Conversely, the PHYDYAS filter achieves higher network SE than Type-I and Type-II filters, highlighting a trade-off between raw error rate and overall throughput efficiency.

3. Optimization Algorithm

To maximize the ergodic sum rate ( $R_S(p)$ ), the paper proposes an online stochastic optimization algorithm (Algorithm 1 in the main paper):

Stochastic Approximation: Since the expectation over channel realizations is not available in closed form, the algorithm uses a stochastic estimate updated iteratively.
Recursive Averaging: The objective function is updated using a weighted average of past instantaneous rate samples. With a step size $\delta(\tau) = 1/(\tau+1)$ , this reduces to the arithmetic mean of observed samples, effectively performing online averaging without storing past channel realizations.
Convergence: The algorithm converges within approximately 100 iterations, as verified numerically.

Key Results and Comparisons

Performance vs. CP-OFDM

Robustness to CFO: Under residual CFO ( $\epsilon = 0.3$ ), the proposed FBMC/QAM system significantly outperforms CP-OFDM in both BER and Network SE. CP-OFDM suffers from severe SE degradation in this scenario, whereas FBMC/QAM maintains robustness.
Interference Breakdown: In Multi-User MIMO (MU-MIMO) scenarios with 8 users and 32 transmit antennas:
- Under Maximum Ratio Transmission (MRT), Multi-User Interference (MUI) is the dominant interference.
- Under Zero-Forcing (ZF), the dominant interference shifts to ICI (specifically for odd subcarriers) and orthogonality loss.

Optimization Efficiency

The proposed online stochastic algorithm is compared against an offline Large Deviation Theory (LDT) based approach [11]:

Data Requirements: The proposed method requires only one channel realization per iteration and does not need a batch of $N$ realizations simultaneously.
Complexity: It avoids the need for external solvers (like CVX) and achieves comparable SE performance with significantly fewer iterations (small vs. large) compared to the LDT-based benchmark.

Significance and Claims

The paper positions its contributions as follows:

Comprehensive Modeling: It provides a unified notation and theoretical derivation for FD FBMC/QAM MIMO systems, explicitly accounting for the complex interplay between self-interference, intrinsic interference, and channel effects.
Filter Design Rationale: It justifies the use of the PHYDYAS filter with a dual-filter structure ( $B=2$ ) as a practical solution that balances orthogonality and interference suppression, while acknowledging that designing a universally optimal filter for FBMC/QAM in multi-user FD settings remains an open research problem.
Algorithmic Efficiency: The proposed stochastic optimization method offers a computationally efficient alternative to offline batch methods, enabling real-time spectral efficiency maximization without prior knowledge of channel statistics or large data buffers.
Waveform Viability: The results demonstrate that FBMC/QAM is a viable candidate for full-duplex MIMO systems, offering superior robustness to frequency offsets and higher spectral efficiency compared to traditional CP-OFDM, despite the challenges of intrinsic interference.

The authors maintain a modest stance, noting that while the current framework uses established filters, future work could explore joint optimization of transmit and receive filters or the development of new prototype filters specifically tailored to the end-to-end fading channel effects in full-duplex scenarios.