Equivalent External Noise Temperature of Time-Varying Receivers

TL;DR

The paper addresses how time-varying receivers alter the external noise temperature by intermodulating out-of-band noise into the observation band. It generalizes the classical antenna noise-temperature framework through a cross-frequency effective aperture, enabling analysis of signals and noise under periodic time variation, including parametric amplification and time-modulated arrays. Key contributions include explicit expressions for $T_A^{ ext{TV}}$ in terms of harmonic apertures $ar{A}_ ext{eff}^p$ and harmonics $p$, comparisons between LTI and TV SNRs, and demonstrative case studies (degenerate parametric amplification and TMAs) showing substantial out-of-band noise coupling and mitigation strategies via filtering. The findings underscore practical design tradeoffs in time-varying systems and provide a pathway for noise analysis and optimization in advanced receivers. Practical impact lies in guiding modulation and filtering choices to balance gain with noise performance in time-varying antennas and architectures.

Abstract

The equivalent external noise temperature of time-varying antennas is studied using the concept of cross-frequency effective aperture, which quantifies the intermodulation conversion of external noise across the frequency spectrum into a receiver's operational bandwidth. The theoretical tools for this approach are laid out following the classical method for describing external noise temperature of linear time-invariant antennas, with generalizations made along the way to capture the effects of time-varying components or materials. The results demonstrate the specific ways that a time-varying system's noise characteristics are dependent on its cross-frequency effective aperture and the broadband noise environment. The general theory is applied to several examples, including abstract models of hypothetical systems, antennas integrated with parametric amplification, and time-modulated arrays.

Figures (8)

• Figure 1: General analysis setup. Noise intensity $\tilde{n}$ impinges upon a receiver from all directions $\boldsymbol{\hat{k}}$, while a signal $\tilde{s}$ is incident from only the $\boldsymbol{\hat{k}}_\mathrm{s}$ direction.
• Figure 2: Depiction of an antenna's cross-frequency effective aperture coupling incoming noise from each modulation harmonic into the observation bandwidth. Assuming a isotropic noise environment, the average terms $\bar{A}_\mathrm{eff}^p$ control the amount of coupling from each harmonic via \ref{['eq:tv-littlepnoise']}.
• Figure 3: Schematic depiction of an example calculation using a flat external brightness temperature (top panel). The incoming spectrum is divided into signal (blue) and noise (red). Markers denote the terms $A_\mathrm{eff}^0$ (circle) and $\bar{A}_\mathrm{eff}^p$ ($\times$). Resulting ratio of TV and LTI SNR levels, in dB (bottom panel).
• Figure 4: Schematic depiction of an example calculation using a non-uniform external brightness temperature (top panel). The incoming spectrum is divided into signal (blue) and noise (red). Markers denote the terms $A_\mathrm{eff}^0$ (circle) and $\bar{A}_\mathrm{eff}^p$ ($\times$). Resulting ratio of TV and LTI SNR levels, in dB (bottom panel).
• Figure 5: Parametrically loaded loop antenna and simplified equivalent circuit model. In simulation, the capacitor and resistor forming the antenna's load are modeled using lumped elements over a single RWG edge, drawn schematically in an exploded view in the geometry drawn above.