[Paper Review] Multiuser Diversity for the Cognitive Uplink with Generalized Fading and Reduced Primary's Cooperation

Ehsan Nekouei, Hazer İnaltekin+1 more|arXiv (Cornell University)|Sep 6, 2012

Advanced MIMO Systems Optimization24 references3 citations

TL;DR

This paper proposes a K-smallest channel gains (K-SCG) feedback protocol to enable efficient multiuser diversity in cognitive uplink networks with limited feedback. It establishes that K-SCG feedback achieves asymptotically optimal sum-rate scaling—log log N in total-power-and-interference-limited networks and log N in interference-limited and individual-power-and-interference-limited networks—when K_N = N^δ (δ ∈ (0,1)) or K_N = O(1), respectively, while keeping primary interference negligible.

ABSTRACT

In cognitive multiple access networks, feedback is an important mechanism to convey secondary transmitter primary base station (STPB) channel gains from the primary base station (PBS) to the secondary base station (SBS). This paper investigates the optimal sum-rate capacity scaling laws for cognitive multiple access networks in feedback limited communication scenarios. First, an efficient feedback protocol called $K$-smallest channel gains ($K$-SCGs) feedback protocol is proposed in which the PBS feeds back the $\K$ smallest out of $N$ STPB channel gains to the SBS. Second, the sum-rate performance of the $K$-SCG feedback protocol is studied for three network types when transmission powers of secondary users (SUs) are optimally allocated. The network types considered are total-power-and-interference-limited (TPIL), interference-limited (IL) and individual-power-and-interference-limited (IPIL) networks. For each network type studied, we provide a sufficient condition on $\K$ such that the $K$-SCG feedback protocol is {\em asymptotically} optimal in the sense that the secondary network sum-rate scaling behavior under the $K$-SCG feedback protocol is the same with that under the full-feedback protocol. We allow distributions of secondary-transmitter-secondary-base-station (STSB), and STPB channel power gains to belong to a fairly general class of distributions called class $\mathcal{C}$-distributions that includes commonly used fading models.

Motivation & Objective

• To address the high feedback overhead in cognitive multiple access networks where secondary base stations require channel state information from primary base stations.
• To investigate sum-rate capacity scaling laws under feedback-limited conditions in cognitive radio networks with generalized fading distributions.
• To design a feedback protocol that maintains optimal sum-rate scaling while minimizing the number of channel gains reported.
• To ensure that the interference at the primary base station remains arbitrarily small without sacrificing secondary network throughput.

Proposed method

• Introduces the K-SCG feedback protocol, where the primary base station reports only the K_N smallest of N secondary-transmitter-to-primary-base-station (STPB) channel gains to the secondary base station.
• Analyzes sum-rate performance under three network models: total-power-and-interference-limited (TPIL), interference-limited (IL), and individual-power-and-interference-limited (IPIL).
• Derives sufficient conditions on K_N such that the K-SCG protocol achieves the same asymptotic sum-rate scaling as full feedback.
• Uses extreme value theory and order statistics to characterize the behavior of the minimum STPB channel gains under general C-distributions, including Rayleigh and Rician fading.
• Applies optimal power allocation strategies at the secondary base station based on the reported K_N channel gains to maximize sum-rate under interference and power constraints.
• Employs lower and upper bounding techniques to establish tight asymptotic sum-rate scaling laws for each network type.

Experimental results

Research questions

• RQ1 What feedback protocol minimizes overhead while preserving optimal sum-rate scaling in cognitive uplink networks with generalized fading?
• RQ2 How does the number of reported channel gains (K_N) affect the secondary network’s sum-rate scaling in different interference regimes?
• RQ3 Can the interference at the primary base station be made arbitrarily small without degrading the secondary network’s sum-rate performance?
• RQ4 What is the optimal scaling behavior of the secondary network sum-rate under K-SCG feedback in TPIL, IL, and IPIL networks?
• RQ5 How does the choice of K_N affect the trade-off between feedback overhead and sum-rate optimality?

Key findings

• In TPIL networks, the K-SCG feedback protocol is asymptotically optimal when K_N = N^δ for δ ∈ (0,1), achieving a sum-rate scaling of (1/n_h) log log N, where n_h is derived from the STSB channel distribution.
• For IL networks, the K-SCG protocol is asymptotically optimal when K_N = O(1), achieving the optimal sum-rate scaling of (1/γ_g) log N, where γ_g is a parameter from the STPB channel distribution.
• In IPIL networks, the K-SCG protocol is asymptotically optimal with K_N = O(1), yielding a sum-rate scaling of min(1, 1/γ_g) log N.
• The average interference power at the PBS can be made arbitrarily small while maintaining the optimal sum-rate scaling behavior in all network types.
• The proposed feedback protocol achieves the same asymptotic sum-rate scaling as full feedback, demonstrating that only a small subset of channel gains is sufficient for optimal performance.
• Numerical results confirm the derived scaling laws hold even for finite N, validating the theoretical analysis across various fading distributions.