Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the Distribution of Matched Filtering with Continuous Aperture Arrays

Amy S. Inwood, Abdulla Firag, Peter J. Smith, Michail Matthaiou

Abstract

Continuous aperture arrays (CAPAs) provide a theoretical upper bound on the performance of densely packed antenna arrays, but their analysis is limited by the lack of closed-form signal-to-noise ratio (SNR) distributions under realistic fading conditions. This paper derives accurate analytical expressions for the matched-filter SNR distribution of one-dimensional CAPAs in correlated Rayleigh environments under both the sinc and Jakes correlation models using the Karhunen-Loeve expansion. By applying a truncated hypoexponential model, we obtain accurate approximations for the probability density function and cumulative distribution function of the SNR that closely match simulations, including the outage probability region where precise characterization is critical. Compared to a standard gamma approximation, our approach provides significantly improved accuracy in this regime. Additionally, the CAPA system considered is shown to outperform discrete antenna arrays. The derived expressions enable tractable and accurate evaluation of CAPAs under practical channel models.

On the Distribution of Matched Filtering with Continuous Aperture Arrays

Abstract

Continuous aperture arrays (CAPAs) provide a theoretical upper bound on the performance of densely packed antenna arrays, but their analysis is limited by the lack of closed-form signal-to-noise ratio (SNR) distributions under realistic fading conditions. This paper derives accurate analytical expressions for the matched-filter SNR distribution of one-dimensional CAPAs in correlated Rayleigh environments under both the sinc and Jakes correlation models using the Karhunen-Loeve expansion. By applying a truncated hypoexponential model, we obtain accurate approximations for the probability density function and cumulative distribution function of the SNR that closely match simulations, including the outage probability region where precise characterization is critical. Compared to a standard gamma approximation, our approach provides significantly improved accuracy in this regime. Additionally, the CAPA system considered is shown to outperform discrete antenna arrays. The derived expressions enable tractable and accurate evaluation of CAPAs under practical channel models.
Paper Structure (15 sections, 2 theorems, 37 equations, 4 figures, 1 table)

This paper contains 15 sections, 2 theorems, 37 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Analysis
  4. KL Expansion of $\gamma_1$
  5. Eigenvalues of the Covariance Function
  6. Sinc Correlation
  7. Jakes Correlation
  8. PDF and CDF of $\gamma_1$
  9. Hypoexponential Distribution
  10. Gamma Variable Correction
  11. Numerical Results
  12. CDF Validation and Impact of Antenna Aperture
  13. PDF Validation and Impact of Carrier Frequency
  14. Outage Probabilities
  15. Conclusion

Key Result

Lemma 1

The $n$-th eigenvalue of $C(x_1,x_2)$ in eq:sinc_corr can be accurately approximated by eq:lambda_sinc, where $A_2=2a_nW$, $C_2=2cW$, $C_p{=}W(c{+}a_n)$ and $C_m{=}W(c{-}a_n)$.

Figures (4)

  • Figure 1: The UL system model for a 1D continuous aperture antenna.
  • Figure 2: CDFs of CAPAs of varying lengths for both correlation models compared with discrete antenna arrays of the same length.
  • Figure 3: The PDFs of CAPAs for correlated Rayleigh channels.
  • Figure 4: The outage probabilities of CAPAs under sinc correlation.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Lemma 2
  • proof