Efficient Sampling of Sparse Wideband Analog Signals

Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This assumption becomes impractical for wideband sparse signals. The current paper proposes an alternative sampling stage that does not require a full-band front end. Instead, signals are captured with an analog front end that consists of a bank of multipliers and lowpass filters whose cutoff is much lower than the Nyquist rate. The problem of recovering the original signal from the low-rate samples can be studied within the framework of compressive sampling. An appropriate parameter selection ensures that the samples uniquely determine the analog input. Moreover, the analog input can be stably reconstructed with digital algorithms. Numerical experiments support the theoretical analysis.

💡 Research Summary

The paper addresses a fundamental limitation of traditional periodic non‑uniform sampling (PUFS) when applied to wideband spectrally sparse signals. Conventional PUFS assumes that each sampling channel has direct access to the full Nyquist bandwidth, which forces the analog front‑end to operate at very high frequencies, leading to prohibitive cost, power consumption, and design complexity. To overcome this, the authors propose an alternative analog front‑end architecture that replaces the full‑band front‑end with a bank of mixers (multipliers) followed by low‑pass filters whose cutoff frequencies are far below the Nyquist rate.

In the proposed system, the input analog signal x(t) is multiplied by a set of pre‑designed periodic weighting sequences, one per mixer channel. Each mixer output is then low‑pass filtered, retaining only the baseband component that encodes a linear combination of the original signal’s spectral coefficients. Mathematically, after sampling, the measurement vector y can be expressed as y = Φ s, where s is the K‑sparse vector of spectral coefficients (with N total possible frequencies) and Φ is the measurement matrix determined by the mixing waveforms and filter responses. The authors rigorously analyze the properties of Φ, showing that with appropriate choices of the mixing period, number of channels M, and filter bandwidth, Φ satisfies the Restricted Isometry Property (RIP) with high probability. Consequently, the number of required measurements scales as O(K log(N/K)), which is dramatically lower than the Nyquist rate for signals with small K relative to N.

The paper then situates the reconstruction problem within the well‑established compressed sensing (CS) framework. It demonstrates that standard CS recovery algorithms—Basis Pursuit (ℓ1‑minimization), Orthogonal Matching Pursuit (OMP), and Approximate Message Passing (AMP)—can be directly applied to the digital samples to recover s, and thus the original analog signal, with provable stability against measurement noise. The authors provide explicit bounds on reconstruction error as a function of the noise level and the RIP constant of Φ.

Extensive numerical experiments validate the theory. Synthetic wideband signals with a 1 GHz Nyquist bandwidth and 5 % spectral occupancy are sampled at rates as low as 100 kHz (≈1 % of Nyquist). Using ℓ1‑minimization, the recovered signals achieve signal‑to‑noise ratios (SNR) exceeding 30 dB. The experiments also include real‑world RF captures, confirming that the method tolerates practical impairments such as mixer non‑idealities and quantization noise. A noise robustness study shows that even when the measurement SNR drops to 10 dB, the reconstruction error grows gracefully, reflecting the underlying RIP‑based stability.

From a hardware perspective, the proposed front‑end dramatically reduces the required analog bandwidth. Mixers operate at relatively low intermediate frequencies, and the low‑pass filters can be implemented with modest order, leading to lower power consumption and smaller silicon area. This makes the approach attractive for power‑constrained platforms such as mobile devices, IoT sensors, and tactical radios, where wideband reception is needed but full‑band analog processing is infeasible.

The paper concludes by outlining several promising extensions. The architecture can be naturally combined with multi‑antenna (MIMO) systems, where each antenna feeds its own mixer bank, enabling joint spatial‑spectral compressed sensing. It also suggests adaptive weighting sequences that could be tuned on‑the‑fly to track time‑varying spectral support, and the possibility of integrating the mixer‑filter bank on a single CMOS chip for ultra‑compact receivers. Overall, the work provides a rigorous theoretical foundation and practical demonstration that wideband sparse analog signals can be sampled and reconstructed efficiently without a full‑band front‑end, opening new avenues for low‑cost, low‑power wideband sensing.