On Ergodic Sum Capacity of Fading Cognitive Multiple-Access and Broadcast Channels (0806.4468v2)

Abstract: This paper studies the information-theoretic limits of a secondary or cognitive radio (CR) network under spectrum sharing with an existing primary radio network. In particular, the fading cognitive multiple-access channel (C-MAC) is first studied, where multiple secondary users transmit to the secondary base station (BS) under both individual transmit-power constraints and a set of interference-power constraints each applied at one of the primary receivers. This paper considers the long-term (LT) or the short-term (ST) transmit-power constraint over the fading states at each secondary transmitter, combined with the LT or ST interference-power constraint at each primary receiver. In each case, the optimal power allocation scheme is derived for the secondary users to achieve the ergodic sum capacity of the fading C-MAC, as well as the conditions for the optimality of the dynamic time-division-multiple-access (D-TDMA) scheme in the secondary network. The fading cognitive broadcast channel (C-BC) that models the downlink transmission in the secondary network is then studied under the LT/ST transmit-power constraint at the secondary BS jointly with the LT/ST interference-power constraint at each of the primary receivers. It is shown that D-TDMA is indeed optimal for achieving the ergodic sum capacity of the fading C-BC for all combinations of transmit-power and interference-power constraints.

• The paper analyzes the ergodic sum capacity of fading cognitive radio networks operating as Multiple-Access (MAC) and Broadcast Channels (BC) under various power and interference constraints.
• A key finding is that Dynamic Time-Division-Multiple-Access (D-TDMA) achieves ergodic sum capacity in cognitive BC channels under different constraint combinations and is optimal in various MAC scenarios.
• Numerical results demonstrate that Long-Term (LT) power constraints generally yield higher ergodic sum capacity compared to Short-Term (ST) constraints due to increased flexibility in resource allocation.

An In-Depth Analysis of the Ergodic Sum Capacity of Fading Cognitive MAC and BC Channels

This paper rigorously investigates the ergodic sum capacity of fading cognitive radio networks within both Multiple-Access Channels (C-MAC) and Broadcast Channels (C-BC). The paper primarily focuses on utilizing the framework of cognitive radio (CR), which allows secondary users to access the spectrum initially designated for primary users while adhering to certain power constraints that aim to protect primary transmissions. Unlike a straightforward opportunistic spectrum access (OSA) method where secondary users only transmit when primary transmissions are nonexistent, this paper investigates a spectrum sharing strategy with an interference-power constraint that ensures the primary network remains unharmed by the secondary transmissions.

Key Contributions and Findings

1. Fading Cognitive MAC and BC: The paper develops an analytical framework for secondary networks, characterized by fading MAC and BC, which models scenarios with multiple secondary users transmitting to a secondary base station (BS), who are constrained by both their transmit powers and the interference imposed on primary receivers.
2. Ergodic Sum Capacity Characterization: The research provides a comprehensive derivation of the optimal power allocation schemes across various transmit-power and interference-power constraints, such as Long-Term (LT) and Short-Term (ST) constraints. It finds that for known fading channel conditions, these constraints have different impacts on the network’s achievable capacity.
3. Dynamic Time-Division-Multiple-Access (D-TDMA) Optimality: One significant insight is the demonstration that D-TDMA achieves ergodic sum capacity in various constraint scenarios. For instance, for C-BC, D-TDMA is shown to be optimal across all considered combinations of transmit and interference-power constraints.
4. Impact of TDMA Constraint: For scenarios involving explicit TDMA constraints, particularly in the fading C-MAC, the paper reveals critical differences in capacity compared to cases without such constraints. This highlights the essential role of multiuser diversity in achieving optimal throughput in cognitive networks.

Numerical Results

The numerical experiments vividly illustrate the impact of different power constraints on the ergodic sum capacity. The results show that configurations with LT constraints generally outperform those with ST constraints, as the former allows more flexible dynamic resource allocation to the secondary users. This flexibility is crucial in environments with channel uncertainties typically found in fading channels.

Implications and Future Directions

From a practical perspective, the insights from this paper allow for better network designs, particularly for cognitive radio networks that aim for efficient spectrum utilization. The findings suggest that cognitive radios equipped with multi-antenna systems could further amplify capacity gains by exploiting additional degrees of freedom offered by spatial multiplexing. Moreover, by characterizing ergodic capacities under various constraint scenarios, this research opens avenues for designing more sophisticated real-time spectrum sharing mechanisms that balance between spectrum utilization efficiency and primary user protection.

Conclusion

Overall, this paper offers a detailed theoretical exploration of the ergodic sum capacity in cognitive MAC and BC channels under various realistic constraints. The work sets a foundation for understanding how CR networks can effectively operate alongside existing radio networks without detrimental interference, highlighting dynamic resource allocation’s critical role within this context. Speculatively, as AI and machine learning strategies continue to evolve, incorporating such technologies might redefine dynamic spectrum access, leveraging real-time learning to optimize even further within these complex environments.