Baseband FM (BBFM): Digital-Analog Integration

• Baseband FM (BBFM) is a communications architecture that directly drives analog FM modulators with digitally encoded pulse trains.
• It integrates advanced digital techniques, including neural encoding and vocoders, to boost audio bandwidth, noise resilience, and interoperability.
• Performance evaluations show BBFM's strengths in handling multipath fading and noise, making it ideal for modern public-safety and commercial networks.

Baseband Frequency Modulation (BBFM) is a communications system architecture in which a multi-level discrete-time pulse train, typically derived from digitally encoded information (such as speech), directly drives a legacy analog FM modulator. The resulting signal is transmitted using standard frequency modulation radio hardware; at the receiver, a standard analog FM demodulator is used, followed by digital post-processing to recover the information. This approach combines the robustness, timing, and synchronization simplicity of analog FM with the flexibility of digital signal processing, and is widely deployed in Land Mobile Radio (LMR) systems, particularly as a bridging architecture where analog and digital radios must interoperate. Recent innovations apply neural representations and advanced codecs to the BBFM channel, yielding substantial improvements in audio bandwidth and noise resilience.

1. BBFM System Architecture

BBFM architectures consist of a digital source encoder, an amplitude mapping or pulse encoding stage, an analog FM modulator, a standard radio-frequency transmission channel (potentially subject to fading), a standard analog FM demodulator, and a digital decoder. The canonical processing chain comprises the following stages:

1. Speech sampling and encoding: Speech is digitized (typically at 8 kHz) and compressed (e.g., via a vocoder) to obtain feature vectors or bit streams.
2. Error protection: Forward error correction (FEC) codes are applied to enhance robustness.
3. Symbol mapping: The coded bit stream is mapped onto a low-order multi-level amplitude sequence (pulse train), often with 2 or 4 levels.
4. Analog FM modulation: The multi-level signal directly drives a standard analog FM modulator, producing a frequency-modulated RF carrier.
5. Reception and demodulation: The FM signal is received and processed using an analog FM demodulator, producing a noisy estimate of the transmitted symbol sequence.
6. Decoding and synthesis: Demodulated symbols are processed by slicers, inverse FEC, and speech decoders or vocoders (including modern neural vocoders such as FARGAN in new systems (Rowe et al., 21 Sep 2025)).

This architecture leverages the channel properties of analog FM—particularly its resilience to timing and frequency errors—while permitting digital information to be transmitted and recovered through the FM modulation process (Rowe et al., 21 Sep 2025).

2. Channel Modeling and Signal Representation

The BBFM channel is characterized by the nonlinear and memory-laden transformation imparted by analog FM modulation and demodulation. The process can be approximated using a linear additive-noise model for many digital communication applications (Rowe et al., 21 Sep 2025):

$\hat{z} = z + n$

where $z$ is the vector of transmitted amplitude shift keyed (ASK) symbols, and $n$ is an additive noise term combining the effects of additive white Gaussian noise (AWGN), multipath fading, and intrinsic FM demodulator noise. The FM demodulator output SNR (for operation above threshold) is formulated classically as

$$\mathrm{SNR} = 3 \beta^2 \langle x^2 \rangle \mathrm{CNR}$$

where $\beta = f_n / f_m$ is the modulation index, $f_n$ is the peak deviation, $f_m$ the maximum modulating frequency, $\langle x^2 \rangle$ is the mean square of transmitted signal, and CNR is the carrier-to-noise ratio (Rowe et al., 21 Sep 2025).

Signal amplitude and channel conditions govern the effective noise power:

$\sigma_s = \frac{A}{\sqrt{\mathrm{SNR}}}$

where $A$ is the amplitude corresponding to the maximum deviation, and $\sigma_s$ sets the per-symbol noise variance.

Under fading and variable receive power, the SNR is modeled piecewise:

$$\mathrm{SNR}_{dB} = \begin{cases} R'_{dBm} + G_{FM}, & R'_{dBm} \geq T_{dBm} \ 3R'_{dBm} + G_{FM} - 2T_{dBm}, & R'_{dBm} < T_{dBm} \end{cases}$$

with $R'_{dBm} = R_{dBm} + H_{dB}$ and $H_{dB} = 20 \log_{10} |H|$, and $|H|$ is the Rayleigh fading envelope (Rowe et al., 21 Sep 2025).

3. Machine Learning Approaches for BBFM Speech Transmission

Recent advancements have replaced the traditional quantization, coding, and mapping chain in BBFM with machine-learned representations (Rowe et al., 21 Sep 2025). A prominent approach is the RADE (Radio AutoDEcoder) system, which employs:

• Feature extraction: Conversion of audio into vocoder features (e.g., 18 Bark-scale cepstral coefficients, pitch, voicing).
• Neural encoder: A neural network (DenseNet-style, with convolutional and GRU layers) transforms feature vectors into continuous ASK symbol vectors, end-to-end trained to optimize channel transmission.
• Channel mapping: The neural encoder output is mapped directly to the analog FM modulator as in legacy BBFM systems.
• Neural decoder and vocoder: The receiver neural network reconstructs features from the noisy symbol stream, and a neural vocoder (FARGAN) synthesizes the audio output.

This approach dispenses with explicit bit mapping, quantization, and FEC by using the end-to-end training loss (measured on vocoder features): $\mathcal{L}(f, \hat{f})$. As a result, the RADE system achieves greater capacity, bandwidth, and noise robustness than conventional BBFM or analog FM schemes (Rowe et al., 21 Sep 2025).

4. Performance Evaluation and Comparative Results

Experimental evaluation in (Rowe et al., 21 Sep 2025) demonstrates that RADE achieves significantly improved speech intelligibility and audio bandwidth compared to legacy analog FM:

• Bandwidth: The RADE system transmits and reconstructs up to 8 kHz audio, compared to 3–4 kHz for analog FM, effectively delivering wideband speech.
• Noise robustness: Automatic speech recognition (ASR) testing (using the Whisper decoder) shows up to a 10 dB gain in word error rate (WER) under fading and AWGN scenarios.
• Multipath resilience: The model explicitly incorporates fading effects ($|H|$ in SNR and noise scaling), with much lower WER variability across deep fades.
• Compatibility: The system operates using commodity UHF radios, with RADE symbols injected at the FM modulator and demodulator interfaces. The RADE system can thus serve as a direct upgrade path for both analog FM and digital LMR systems that use BBFM architecture, with no need to modify the RF hardware chain.

Measured SNR, bandwidth, and error performance metrics derive from realistic simulations and hardware-in-the-loop trials employing synthetic fading profiles and channel impairment emulators (Rowe et al., 21 Sep 2025).

5. Relationship to All-Digital and Quadrature-Modulation Models

A distinct but related strand in the literature examines the exact baseband modeling of quadrature-modulated all-digital transmitters (ADT) (Tanovic et al., 2017). This analysis demonstrates that such transmitters—whose hardware can closely resemble BBFM systems in their use of pulse encoding and nonlinear switched-mode power amplifiers—can be exactly modeled at baseband via a cascade of a pulse encoder, a discrete-time Volterra series (short-memory, nonlinear), and a long-memory linear filter. The cascade can be expressed as:

$$\mathcal{S} = \mathcal{P} \rightarrow \mathcal{V} \rightarrow \mathcal{L} \rightarrow \mathcal{K}$$

where $\mathcal{P}$ is the pulse encoder, $\mathcal{V}$ implements Volterra monomials over the input sequence, $\mathcal{L}$ is a long-memory linear time-invariant filter (approximated via FIR), and $\mathcal{K}$ is a downsampler to manage distinct sampling rate domains. This model is leveraged to construct efficient digital predistortion (DPD) architectures, exploiting the separation of nonlinear short-term and linear long-term distortion, crucially relevant to BBFM implementations where residual nonlinearity and filtering effects may dominate (Tanovic et al., 2017). MATLAB simulations show modeling errors below 0.1% (–20 dB) for typical radio hardware parameters.

6. Alternate BBFM Reception Paradigms

Alternative to classical and neural BBFM architectures, quantum-optical receivers based on cesium Rydberg atomic vapors have been demonstrated for direct, high-sensitivity baseband FM demodulation (Jiao et al., 2018, Anderson et al., 2018). These receivers operate by mapping the instantaneous amplitude and frequency deviations of a gigahertz-range microwave carrier into measurable changes in the Autler–Townes splitting of an atomic Electromagnetically Induced Transparency (EIT) spectrum. Key findings include:

• Non-electronic, SI-traceable demodulation with sensitivity to both AM and FM modulation, covering carrier frequencies from ~1 GHz to hundreds of GHz.
• In FM operation, the instantaneous frequency deviation is mapped to the asymmetry of the AT spectral peaks, which can be analyzed to recover the baseband modulating signal.
• Demonstrated baseband bandwidths reach up to 100 kHz, with main limitations arising from the spectroscopic readout speed and optical noise sources.
• These systems support multi-band operation and high field sensitivity, presenting an alternative architecture for environments hostile to traditional antennas (Anderson et al., 2018).

7. Practical Considerations and Deployment Implications

BBFM enables backward-compatible upgrades to digital communications over legacy FM infrastructure with minimal hardware changes. The modulation/demodulation process tolerates significant distortion, timing errors, and channel-induced impairments, especially when augmented with advanced signal representations such as those obtained from radio autoencoders. Empirical deployment over commodity UHF radios confirms feasibility for public-safety and commercial networks, and suggests extendibility to high-fidelity wideband speech applications.

A plausible implication is the progressive replacement of traditional quantization and FEC subsystems with learned continuous-channel representations, contingent on computational resource availability and regulatory compliance. Quantum-optical BBFM receivers, while not commercially mainstream, illustrate a limit case in sensitivity and spectral purity.

The generality of BBFM architectures, including unconstrained pulse encoding and multilevel modulation, enables deployment in a diverse range of wireless links, bridging historical analog radio and emerging neural communications paradigms.