# Spectral and Energy Efficiency in Cognitive Radio Systems with Unslotted Primary Users and Sensing Uncertainty

## TL;DR

This paper investigates energy efficiency and throughput optimization in cognitive radio systems with unslotted primary users, considering sensing errors and collision constraints, and proposes algorithms for optimal power and frame duration.

## Contribution

It introduces optimal power control policies and low-complexity algorithms for maximizing energy efficiency and throughput under sensing errors and collision constraints.

## Key findings

- Optimal power control policies are derived for EE and throughput maximization.
- Impact of sensing errors on EE, throughput, and collision metrics is quantified.
- Tradeoffs between EE and throughput under various primary user traffic conditions are analyzed.

## Abstract

This paper studies energy efficiency (EE) and average throughput maximization for cognitive radio systems in the presence of unslotted primary users. It is assumed that primary user activity follows an ON-OFF alternating renewal process. Secondary users first sense the channel possibly with errors in the form of miss detections and false alarms, and then start the data transmission only if no primary user activity is detected. The secondary user transmission is subject to constraints on collision duration ratio, which is defined as the ratio of average collision duration to transmission duration. In this setting, the optimal power control policy which maximizes the EE of the secondary users or maximizes the average throughput while satisfying a minimum required EE under average/peak transmit power and average interference power constraints are derived. Subsequently, low-complexity algorithms for jointly determining the optimal power level and frame duration are proposed. The impact of probabilities of detection and false alarm, transmit and interference power constraints on the EE, average throughput of the secondary users, optimal transmission power, and the collisions with primary user transmissions are evaluated. In addition, some important properties of the collision duration ratio are investigated. The tradeoff between the EE and average throughput under imperfect sensing decisions and different primary user traffic are further analyzed.