Decentralized Fair Scheduling in Two-Hop Relay-Assisted Cognitive OFDMA Systems

In this paper, we consider a two-hop relay-assisted cognitive downlink OFDMA system (named as secondary system) dynamically accessing a spectrum licensed to a primary network, thereby improving the efficiency of spectrum usage. A cluster-based relay-assisted architecture is proposed for the secondary system, where relay stations are employed for minimizing the interference to the users in the primary network and achieving fairness for cell-edge users. Based on this architecture, an asymptotically optimal solution is derived for jointly controlling data rates, transmission power, and subchannel allocation to optimize the average weighted sum goodput where the proportional fair scheduling (PFS) is included as a special case. This solution supports decentralized implementation, requires small communication overhead, and is robust against imperfect channel state information at the transmitter (CSIT) and sensing measurement. The proposed solution achieves significant throughput gains and better user-fairness compared with the existing designs. Finally, we derived a simple and asymptotically optimal scheduling solution as well as the associated closed-form performance under the proportional fair scheduling for a large number of users. The system throughput is shown to be $\mathcal{O}\left(N(1-q_p)(1-q_p^N)\ln\ln K_c\right)$, where $K_c$ is the number of users in one cluster, $N$ is the number of subchannels and $q_p$ is the active probability of primary users.

💡 Research Summary

The paper addresses the problem of efficiently sharing licensed spectrum with a primary network by means of a two‑hop relay‑assisted cognitive downlink OFDMA system, referred to as the secondary system. The authors propose a cluster‑based architecture in which each cluster contains a dedicated relay station (RS). The base station (BS) communicates with the RS, which in turn serves the users (UEs) within its cluster. This topology reduces the direct interference from the BS to primary users (PUs) because the RS can sense PU activity on each sub‑channel and adapt its transmission power or avoid the sub‑channel altogether.

The core technical contribution is a joint optimization of three control variables: per‑user data rates, transmit powers, and sub‑channel assignments. The objective is to maximize the average weighted sum goodput, a metric that captures the amount of successfully delivered data while incorporating a weight for each user. By selecting the weights appropriately, the formulation includes proportional‑fair scheduling (PFS) as a special case, thereby guaranteeing long‑term fairness among users, especially those at the cell edge.

The optimization problem is subject to several realistic constraints: (i) each sub‑channel can be assigned to at most one user, (ii) total transmit power limits at the BS and RS, (iii) interference constraints that bound the expected interference power caused to active PUs, and (iv) robustness requirements that account for imperfect channel state information at the transmitter (CSIT) and noisy sensing measurements. Because the problem mixes integer (sub‑channel assignment) and continuous (power, rate) variables, a direct solution would be computationally prohibitive.

To overcome this, the authors derive an asymptotically optimal solution that becomes exact as the number of users per cluster, (K_c), grows large. Using Lagrangian dual decomposition, the global problem is split into independent sub‑problems for each cluster. Each RS solves its local sub‑problem using only locally available CSI and PU activity statistics, while a small set of dual variables (price for power and price for interference) are exchanged with the BS. The resulting power allocation has a water‑filling‑like structure:

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