Optimal Power Allocation for Fading Channels in Cognitive Radio Networks: Ergodic Capacity and Outage Capacity (0808.3689v2)

Abstract: A cognitive radio network (CRN) is formed by either allowing the secondary users (SUs) in a secondary communication network (SCN) to opportunistically operate in the frequency bands originally allocated to a primary communication network (PCN) or by allowing SCN to coexist with the primary users (PUs) in PCN as long as the interference caused by SCN to each PU is properly regulated. In this paper, we consider the latter case, known as spectrum sharing, and study the optimal power allocation strategies to achieve the ergodic capacity and the outage capacity of the SU fading channel under different types of power constraints and fading channel models. In particular, besides the interference power constraint at PU, the transmit power constraint of SU is also considered. Since the transmit power and the interference power can be limited either by a peak or an average constraint, various combinations of power constraints are studied. It is shown that there is a capacity gain for SU under the average over the peak transmit/interference power constraint. It is also shown that fading for the channel between SU transmitter and PU receiver is usually a beneficial factor for enhancing the SU channel capacities.

• The paper proposes novel power allocation strategies under both peak and average constraints to maximize ergodic and outage capacities in CRNs.
• It employs advanced optimization techniques and dual variable methods across multiple fading models, including Rayleigh and Nakagami.
• The results demonstrate that average interference constraints yield higher secondary user capacities compared to strict peak constraints.

Optimal Power Allocation for Fading Channels in Cognitive Radio Networks: Ergodic Capacity and Outage Capacity

The paper addresses the critical challenge of optimizing power allocation in Cognitive Radio Networks (CRNs) under various constraints. It specifically focuses on maximizing the ergodic capacity and outage capacity of secondary user (SU) channels in scenarios where both transmit and interference power constraints are considered.

Overview

Cognitive Radio (CR) technology offers an efficient approach to ameliorate spectrum under-utilization by allowing secondary users to access the spectrum opportunistically. This paper evaluates the scenario where SUs coexist with primary users (PUs) by adhering to interference constraints, a strategy known as spectrum sharing. The authors investigate optimal power allocation strategies to attain the ergodic and outage capacities under different fading models and power constraints.

Methodology

The research considers several combinations of power constraints, including peak and average constraints on both transmit and interference powers. For each power constraint scenario, the paper derives optimal power allocation strategies using sophisticated mathematical formulations and optimization techniques:

• Peak Transmit and Peak Interference Power Constraints: The SU maximizes capacity by transmitting at the highest permissible power until interference thresholds are met.
• Peak Transmit and Average Interference Power Constraints: The allocation is dynamic, governed by the average constraint through dual variable techniques.
• Average Transmit and Peak Interference Power Constraints: A cap is placed on power allocation based on interference thresholds, which allows more flexibility when channel degradation is detected.
• Average Transmit and Average Interference Power Constraints: The solution explores joint constraints, yielding a more adaptable power control scheme suitable for various fading conditions.

The paper extensively addresses the different channel fading models including Rayleigh, Nakagami, and Log-normal, providing detailed closed-form solutions and performance results for each.

Numerical and Analytical Results

The paper offers comprehensive numerical simulations and analytical evaluations highlighting several key findings:

1. Capacities with Different Constraints: The paper confirms capacity gains for average constraints over peak constraints, emphasizing the benefits of average interference power constraints in enhancing SU capacity.
2. Impact of Fading Models: Fading between SU and PU often serves as a capacity-enhancing factor, notably in Rayleigh and Nakagami fading scenarios.
3. Delay-Limited Capacity: For delay-sensitive applications, the paper calculates delay-limited capacities, showing how certain channel models, like Rayleigh fading, contribute to zero delay-limited capacity.
4. Outage Capacity: Optimization under outage probability considerations reveals that peak constraints lead to more restrictive power allocations compared to average constraints, with significant differences noted across fading models.

Implications and Future Work

The implications of this research extend to both theoretical and practical domains. The findings advance our understanding of power control in CRNs, suggesting methods to efficiently exploit spectral opportunities. This work lays a foundation for future studies that might explore CR systems with more complex network topologies, enhanced environmental modeling, or real-time adaptation mechanisms in dynamic spectrum access paradigms.

Additionally, this research invites future inquiries into the integration of machine learning to predict and optimize spectrum sharing under diverse operational conditions, potentially leading to even greater improvements in capacity and network reliability.

In summary, this paper contributes a robust framework for optimizing power allocation in CRNs, with significant implications for enhancing spectrum efficiency and network performance in wireless communication systems.