# Energy Efficiency Analysis of Collaborative Compressive Sensing Scheme in Cognitive Radio Networks

## TL;DR

This paper analyzes the energy efficiency of collaborative compressive sensing in cognitive radio networks, deriving optimal parameters to balance energy consumption and detection accuracy, and demonstrating that collaboration can recover compression losses.

## Contribution

It formulates and solves a non-convex optimization problem for maximizing energy efficiency, providing approximations that simplify analysis with negligible errors.

## Key findings

- Energy efficiency can be maximized through optimal parameter selection.
- Collaboration compensates for compression losses, enhancing overall efficiency.
- Tradeoff between sensing accuracy and energy saving is analytically characterized.

## Abstract

In this paper, we investigate the energy efficiency of conventional collaborative compressive sensing (CCCS) scheme, focusing on balancing the tradeoff between energy efficiency and detection accuracy in cognitive radio environment. In particular, we derive the achievable throughput, energy consumption and energy efficiency of the CCCS scheme, and formulate an optimization problem to determine the optimal values of parameters which maximize the energy efficiency of the CCCS scheme. The maximization of energy efficiency is proposed as a multi-variable, non-convex optimization problem, and we provide approximations to reduce it to a convex optimization problem. We highlight that errors due to these approximations are negligible. Later, we analytically characterize the tradeoff between dimensionality reduction and collaborative sensing performance of the CCCS scheme -- the implicit tradeoff between energy saving and detection accuracy, and show that the loss due to compression can be recovered through collaboration which improves the overall energy efficiency.